Find the P-value for the indicated hypothesis test. An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 19 were no-shows. Find the P-value for a test of the airline's claim.

A. 0.3508
B. 0.2061
C. 0.0746
D. 0.1230

Answer:

We use the Binomial Distribution   where p =.84 then probability will be 0.931.

Step-by-step explanation:

P(X≥ 2) = P(X=2) + P (X=3)

           = (³₂)(.84)^2(.16) +  (³3)(.84)^3(.16)⁰

           ≅ 0.931

Hence 0.931 is the answer.

The probability that at least two out of three items chosen randomly are in perfect condition, given that the chance for a randomly chosen item being perfect is 84%, is 97% or 0.97 in decimal form.

This is a question about the probability that we call binomial probability. Here we have to find the probability that at least two out of three randomly chosen items are in perfect condition while the likelihood of a random item being in perfect condition is 84%.

There are two scenarios in which the lot will be accepted: (1) exactly two of the products are perfect, and (2) all three products are perfect.

1. Two products are perfect (using binomial probability formula):

Prob(Two perfect) = 3C2 * (0.84)^2 * (1-0.84)^1 = 0.38

2. All three are perfect:

Prob(Three perfect) = 3C3 * (0.84)^3 * (1 - 0.84)^0 = 0.59

Thus, adding these probabilities gives the total probability that either two or three products are in good condition, which would result in the lot being accepted:

Total Probability = 0.38 + 0.59 = 0.97 or 97%

https://brainly.com/question/33993983

#SPJ3

Answer:

E. None of the above answers is correct

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have [tex]5[/tex] groups and on each group from [tex]j=1,\dots,20[/tex] we have [tex]20[/tex] individuals on each group we can define the following formulas of variation:  

[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]

[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]

[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]

And we have this property

[tex]SST=SS_{between}+SS_{within}[/tex]

The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k-1=5-1=4[/tex] where k =5 represent the number of groups.

The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-K=5*20-5=95[/tex].

And the total degrees of freedom would be [tex]df=N-1=5*20 -1 =99[/tex]

On this case the correct answer would be 4 for the numerator and 95 for the denominator.

E. None of the above answers is correct

Final answer:

To assess whether there is more variation in the first population than in the second, calculate the F-statistic using the ratio of the squares of the sample standard deviations and compare it to the critical F-value at the 0.01 significance level. A calculated F-value significantly greater than 1 suggests greater variation in the first population, but the final decision depends on comparing the F-value to the F-distribution table.

Explanation:

To determine whether there is more variation in the first population at the 0.01 significance level, we can use an F-test for the comparison of two variances given that the populations are normally distributed. We begin by calculating the F-statistic, which is the ratio of the squares of the two sample standard deviations. The formula we use is:

F = (S1)2 / (S2)2

For the given data, the first population standard deviation is 12 and the second is 7, so we calculate the F-statistic as:

F = (122) / (72) = 144 / 49 = 2.9388

An F-value significantly greater than 1 suggests that the variance in the first population is greater than that in the second population. To determine if this observed F-value is statistically significant, we compare it to the critical value of F for the given degrees of freedom at the chosen significance level. However, critical F-values are obtained from statistical tables or software, and as we do not have the specific value for the degrees of freedom here, we cannot make the final comparison.

If the calculated F-value exceeds the critical value from an F-distribution table, we would reject the null hypothesis and conclude that there is more variation in the first population. If it does not exceed the critical value, we would not reject the null hypothesis.

Answer:

The 99% confidence interval for the mean would be (301.064;333.336) mA  

Step-by-step explanation:

1) Notation and some definitions

n=10 sample selected

[tex]\bar x=317.2mA[/tex] sample mean for the sample tubes selected

[tex]s=15.7mA[/tex] sample deviation for the sample selected

Confidence = 99% or 0.99

[tex]\alpha=1-0.99=0.01[/tex] significance level

A confidence interval for the mean is used to "places boundaries around an estimated [tex]\bar X[/tex] so that the true population mean [tex]\mu[/tex] would be expected to lie within those boundaries with a confidence specified. If the uncertainty is large, then the interval between the boundaries must be wide; if the uncertainty is small, then the interval can be narrow"

2) Formula to use

For this case the sample size is <30 and the population standard deviation [tex]\sigma[/tex] is not known, so for this case we can use the t distributon to calculate the critical value. The first step would be calculate alpha

[tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], then we can calculate the degrees of freedom given by:

[tex]df=n-1=10-1=9[/tex]

Now we can calculate the critical value [tex]t_{\alpha/2}=3.25[/tex]

And then we can calculate the confidence interval with the following formula

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]  (1)

3) Calculate the interval

Using the formula (1) and replacing the values that we got we have:

[tex]317.2 - 3.25\frac{15.7}{\sqrt{10}}=301.064[/tex]  

[tex]317.2 + 3.25\frac{15.7}{\sqrt{10}}=333.336[/tex]

So then the 99% confidence interval for the mean would be (301.064;333.336)mA  

Interpretation: A point estimate for the true mean of brightness level for the tubes in the population is 317.2mA, and we are 99% confident that the true mean is between 301.064 mA and 333.336 mA.

Answer: d) 0.31

Step-by-step explanation:

Given : In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 5.4 minutes.

i.e. [tex]\mu=42.5[/tex] and [tex]\sigma= 5.4[/tex]

It is assumed that this is a normally distributed variable.

Let x denotes the time spend by a person on treadmill.

Then, the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

[tex]P(30<x<40)=P(\dfrac{30-42.5}{5.4}<\dfrac{x-\mu}{\sigma}<\dfrac{40-42.5}{5.4})\\\\\approxP(-2.31<z<0.46)\\\\=P(z<-0.46)-P(z<-2.31)\ \ [\because\ P(z_1<z<z_2)=P(z<z_2)-P(z<z_1)]\\\\=1-P(z<0.46)-(1-P(z\leq2.31))\ \ [\because P(Z>z)=1-P(Z\leq z)]\\\\=1-0.6772419-(1-0.9895559)\ \ \text{[By using z-table or calculator]}\\\\=0.3227581-0.0104441=0.312314\approx0.31[/tex]

Hence, the required probability = 0.31

Thus , the correct answer = d) 0.31

Answer:

a. categorical

b. 1018

c. 28.98%

d.  Most voters interviewed are against the new tax

Step-by-step explanation:

Hello!

There was a poll made to know the voter opinion on a law that would increase the gas tax to 20 cents per gallon, this money is going to use for road and bridges improvement and build more mass transportation in the state.

Data:

295 support

672 against

51 no opinion

a. The study variable is "Opinion of the votes on the new gas tax" Categorized: "support; against; no opinion"

This is a categorical variable, that can take one number on a limited amount of possibles values, assigning each observation to a group of nominal categories based on a qualitative feature.

In this case, each voter is assigned to a category according to their opinion on the new tax.

b. To know the sample size you have to add the subtotals of each category:

n= 295 + 672 + 51 = 1018

c. To calculate the percentage of people supporting the new tax, you have to divide the subtotal by the total and multiply it by 100

[tex](\frac{295}{1018})*100[/tex] = 28.978% ≅ 28.98%

d. To answer this it's better to calculate the percentage of each category:

Support: 28.98%

Against: 66.01%

No opinion: 5.01%

Since the category "against" has the greater percentage, you can say that most voters interviewed are against the new gas tax

I hope it helps!

Answer:

the 90% confidence interval to estimate mu = (118.51 ounces, 124.29 ounces) means that out of all the data 90% of the sample has the weight between the range 118.51 ounces and 124.29 ounces.

Step-by-step explanation:

Data provided in the question:

Confidence level = 90%

90% confidence interval to estimate mu = (118.51 ounces, 124.29 ounces)

Now,

The confidence level tells us that out of all the value of the sample the given percentage of confidence level lies within the calculated interval.

Here in the given question,

the 90% confidence interval to estimate mu = (118.51 ounces, 124.29 ounces) means that out of all the data 90% of the sample has the weight between the range 118.51 ounces and 124.29 ounces.

To test if the proportion of college graduates who believe in evolution differs significantly from the proportion of individuals with some college education, we can use the z-test statistic.

To test if there is evidence that the proportion of college graduates who believe in evolution differs significantly from the proportion of individuals with some college education who believe in evolution, we can use the z-test statistic. The formula for the z-test statistic is z = (p1 - p2) / sqrt(pq((1/n1) + (1/n2))), where p1 and p2 are the proportions of college graduates and individuals with some college education who believe in evolution, n1 and n2 are the respective sample sizes, and q = 1 - p. Plugging in the given values, we have z = (0.459- 133/325 - 121/228) / sqrt(0.459 * (1-0.459) * ((1/325) + (1/228))). Calculating this expression will give us the z-test statistic.

https://brainly.com/question/34795811

#SPJ11

The critical t values are reject the null hypothesis and shut down the process.

The correct option is (A).

To find the critical t values for a one-tailed t-test with a significance level of [tex]\( \alpha = 0.10 \)[/tex], we need to look up the t-distribution table or use statistical software.

Since we have a sample size of 17, the degrees of freedom ( df ) for the t-test will be [tex]\( n - 1 = 17 - 1 = 16 \).[/tex]

For a one-tailed t-test with a significance level of [tex]\( \alpha = 0.10 \)[/tex] and 16 degrees of freedom, we find the critical t value.

From the t-distribution table or using statistical software, the critical t value for [tex]\( \alpha = 0.10 \) and \( df = 16 \)[/tex] is approximately 1.337.

So, the critical t values are approximately [tex]\( \pm 1.337 \).[/tex]

Now, we compare the calculated t value for the sample mean to these critical values. If the calculated t value falls beyond these critical values, we reject the null hypothesis.

Since the problem does not provide the calculated t value, we cannot determine whether to reject the null hypothesis or not.

However, based on the information given, we can see that the mean weight of the USB flash drives in the last sample is 31.9 grams, which is heavier than the expected mean weight of 30 grams. If the calculated t value corresponds to a significantly larger value than the critical t value, we may reject the null hypothesis and conclude that the mean weight is significantly different from 30 grams, potentially leading to shutting down the process for adjustment.

Therefore, the correct answer would be:

A. reject the null hypothesis and shut down the process.

Since |4.35| > 1.746, we reject the null hypothesis and conclude that the mean weight of the USB flash drives is significantly different from 30 grams. Therefore, the correct answer is: A. reject the null hypothesis and shut down the process.

To find the critical t-values for a significance level of [tex]\( \alpha = 0.10 \)[/tex] and a sample size of n = 17, we can use a t-distribution table or a statistical software.

For a two-tailed test at a significance level of [tex]\( \alpha = 0.10 \)[/tex] and degrees of freedom df = n - 1 = 17 - 1 = 16, we need to find the critical t-values that correspond to the upper and lower tails of the t-distribution.

Using a t-distribution table or a statistical software, the critical t-values for a significance level of [tex]\( \alpha = 0.10 \)[/tex] and 16 degrees of freedom are approximately [tex]\( t_{\alpha/2} = \pm 1.746 \).[/tex]

So, the critical t-values are approximately[tex]\( \pm 1.746 \).[/tex]

Now, let's compare the calculated t-value with the critical t-values:

The calculated t-value is given by:

[tex]\[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \][/tex]

Where:

- [tex]\( \bar{x} \)[/tex] is the sample mean (31.9 grams)

- [tex]\( \mu \)[/tex] is the population mean (30 grams)

- s is the sample standard deviation (1.8 grams)

- n is the sample size (17)

Substitute the given values:

[tex]\[ t = \frac{31.9 - 30}{\frac{1.8}{\sqrt{17}}} \]\[ t \approx \frac{1.9}{\frac{1.8}{4.123}} \]\[ t \approx \frac{1.9}{0.437} \]\[ t \approx 4.35 \][/tex]

Since |4.35| > 1.746, we reject the null hypothesis and conclude that the mean weight of the USB flash drives is significantly different from 30 grams. Therefore, the correct answer is:

A. reject the null hypothesis and shut down the process.

Answer:

See below

Step-by-step explanation:

We start by dividing the interval [0,4] into n sub-intervals of length 4/n

[tex][0,\displaystyle\frac{4}{n}],[\displaystyle\frac{4}{n},\displaystyle\frac{2*4}{n}],[\displaystyle\frac{2*4}{n},\displaystyle\frac{3*4}{n}],...,[\displaystyle\frac{(n-1)*4}{n},4][/tex]

Since f is increasing in the interval [0,4], the upper sum is obtained by evaluating f at the right end of each sub-interval multiplied by 4/n.

Geometrically, these are the areas of the rectangles whose height is f evaluated at the right end of the interval and base 4/n (see picture)

[tex]\displaystyle\frac{4}{n}f(\displaystyle\frac{1*4}{n})+\displaystyle\frac{4}{n}f(\displaystyle\frac{2*4}{n})+...+\displaystyle\frac{4}{n}f(\displaystyle\frac{n*4}{n})=\\\\=\displaystyle\frac{4}{n}((\displaystyle\frac{1*4}{n})^2+3+(\displaystyle\frac{2*4}{n})^2+3+...+(\displaystyle\frac{n*4}{n})^2+3)=\\\\\displaystyle\frac{4}{n}((1^2+2^2+...+n^2)\displaystyle\frac{4^2}{n^2}+3n)=\\\\\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12[/tex]

but  

[tex]1^2+2^2+...+n^2=\displaystyle\frac{n(n+1)(2n+1)}{6}[/tex]

so the upper sum equals

[tex]\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12=\displaystyle\frac{4^3}{n^3}\displaystyle\frac{n(n+1)(2n+1)}{6}+12=\\\\\displaystyle\frac{4^3}{6}(2+\displaystyle\frac{3}{n}+\displaystyle\frac{1}{n^2})+12[/tex]

When [tex]n\rightarrow \infty[/tex] both [tex]\displaystyle\frac{3}{n}[/tex] and [tex]\displaystyle\frac{1}{n^2}[/tex] tend to zero and the upper sum tends to

[tex]\displaystyle\frac{4^3}{3}+12=\displaystyle\frac{100}{3}[/tex]

64

Step-by-step explanation:

We will divide the volume of the larger cube with that if the smaller cube. However, we’ll first have to convert them to the same SI units;

12 inches  = 1 foot

Therefore the volume of the larger cube;

12 * 12 * 12 = 1728 inches cubed

The volume of the smaller cube;

3 * 3 * 3 = 27 inches cubed

Divide the two;

1728/27

= 64

Learn More:

https://brainly.com/question/12012162

https://brainly.com/question/3531012

https://brainly.com/question/479684

#LearnWithBrainly

Answer:

(a)

[tex]a_{1} = 88.000 \ million\\a_{2} = 94.160 \ million\\a_{3} = 100.751 \ million\\a_{4} = 107.804 \ million\\a_{n} = 82.243*1.07^n\\[/tex]

(b) 2024

Step-by-step explanation:

Global oil consumption in 2011 is given by:

[tex]C_{2011} =\frac{88}{1.07}=82.243 \ million[/tex]

(a) Assuming a constant growth of 0.7% per year, the formula for the daily oil consumption n years after 2011 is:

[tex]a_{n} = a_{0}*1.07^n\\a_{0} = C_{2011} = 82.243\\a_{n} = 82.243*1.07^n[/tex]

The terms a_1, a_2,a_3 and a_4, corresponding to the global oil consumption in the years of 2012, 2013, 2014 and 2015, respectively, are given by:

[tex]a_{1} = 82.243*1.07^1\\a_{1} = 88.000 \ million\\a_{2} = 82.243*1.07^2\\a_{2} = 94.160 \ million\\a_{3} = 82.243*1.07^3\\a_{3} = 100.751 \ million\\a_{4} = 82.243*1.07^4\\a_{4} = 107.804 \ million\\[/tex]

(b) To find the in year in which consumption reaches 195 million barrels a day, apply logarithmic properties:

[tex]a_{n} = 82.243*1.07^n\\ln(a_{n}) = ln(82.243)+ n*ln(1.07)\\\\n=\frac{ln(195)-ln(82.243)}{ln(1.07)} \\n= 12.760[/tex]

Consumption will reach 195 million barrels, 12.7 years after 2011, round it to the next whole year to find when consumption exceeds 195 million:

[tex]Y = 2011+13 = 2024[/tex]

Answer:

Option A) One tailed test is a hypothesis test in which rejection region is in one tail of the sampling distribution

Step-by-step explanation:

One Tailed Test:

[tex]H_0: \bar{x} = \mu\\H_A: \bar{x} < \mu\text{ or } \bar{x} > \mu[/tex]

Thus, for one tailed test,

Option A) One tailed test is a hypothesis test in which rejection region is in one tail of the sampling distribution

Final answer:

A one-tailed test is a hypothesis test where the rejection region is in one tail of the sampling distribution, and is used when the research hypothesis is directional, testing the possibility of a relationship in one direction only. (Option a)

Explanation:

A one-tailed test is a hypothesis test in which the rejection region is in one tail of the sampling distribution. This means that the correct answer to the student's question is a. hypothesis test in which rejection region is in one tail of the sampling distribution. In a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction (which would be the criterion of a two-tailed test).

Depending on the research hypothesis, the rejection region could be in the lower tail (option c) or the upper tail (option d) of the probability distribution. For example, if the alternative hypothesis is HA: X > μ, we are performing a right-tailed test and rejects the null hypothesis if the test statistic falls in the upper tail (right side) of the distribution. If the alternative hypothesis is HA: X < μ, it is a left-tailed test and the rejection region would be in the lower tail (left side).

Answer:

[tex]y = - 2x + 2[/tex]

Step-by-step explanation:

Explained all in my picture

Answer:

-2

Step-by-step explanation:

y2-y1/x2-x1 = -4-4/3-(-1) = -8/3+1 = -8/4 = -2/1 = -2

Answer:

Option C) Rolle's theorem applies

[tex]c = \displaystyle\frac{-4}{3}[/tex]

Step-by-step explanation:

We are given that:

[tex]f(x) = (x + 3)(x - 2)^2[/tex]

Closed interval: [-3,2]

Rolle's Theorem:

According to this theorem if the given function

the, there exist c in (a,b) such that

[tex]f'(c) = 0[/tex]

Continuity of function:

Since the given function is a continuous function, it is continuous everywhere. Therefore, f(x) is continuous in [-3,2]

Differentiability of function:

A polynomial function is differentiable For all arguments. Therefore, f(x) is differentiable in (-3,2)

Now, we evaluate f(-3) and f(2)

[tex]f(x) = (x + 3)(x - 2)^2\\f(-3) = (-3+3)(-3-2)^2 = 0\\f(2) - (2+3)(2-2)^2 = 0\\\Rightarrow f(-3) = f(2) = 0[/tex]

Thus, Rolle's theorem applies on the given function f(x).

According to Rolle's theorem there exist c in (a,b) such that f'(c) = 0

[tex]f(x) = (x + 3)(x - 2)^2\\f'(x) = (x-2)^2 + 2(x+3)(x-2) = 3x^2-2x-8\\f'(c) = 0\\f'(c) = 3c^2-2c-8 = 0\\\Rightarrow (c-2)(3c+4) = 0\\\Rightarrow c = 2, c = \displaystyle\frac{-4}{3}[/tex]

c should lie in (-3,2)

Thus,

[tex]c = \displaystyle\frac{-4}{3}[/tex]

Final answer:

Rolle's Theorem can be applied to the function f(x) = (x + 3)(x - 2)^2 on the closed interval {-3, 2}, and the number c in the open interval (-3, 2) where f'(c) = 0 is c = -4/3.

Explanation:

To determine whether Rolle's Theorem can be applied to the function f(x) = (x + 3)(x - 2)^2 on the closed interval {-3, 2}, we need to check if the function satisfies the three conditions for Rolle's Theorem:

First, note that the function f(x) = (x + 3)(x - 2)^2 is a polynomial function, and all polynomial functions are continuous and differentiable for all real numbers. Therefore, condition 1 is satisfied. Next, we find the derivative of f(x):

f'(x) = (2x-4)(x-2)+(x+3)(2(x-2)) = 4x^2 - 12x + 8 + 2x^2 - 2x - 12 = 6x^2 - 14x - 4.

To find the values of c in the open interval (-3, 2) where f'(c) = 0, we set f'(x) = 0:

6x^2 - 14x - 4 = 0.

We can solve this quadratic equation using factoring, the quadratic formula, or by completing the square. Solving the equation, we find the roots as x = -4/3 and x = 2/3. However, only the root x = -4/3 is in the interval (-3, 2). So, Rolle's Theorem can be applied, and the number c in the open interval (-3, 2) where f'(c) = 0 is c = -4/3.

Answer:

Chrissy walked 1/4 miles on Monday and Tuesday combined.

Step-by-step explanation:

1/8+1/8=2/8

2/8=1/4 you take half of both sides to get the lowest terms using simplification.

Answer: (47.51, 54.49)

Step-by-step explanation:

Confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

, where n= sample size .

[tex]\sigma[/tex] = population standard deviation.

[tex]\overline{x}[/tex] = sample mean

[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex] (significance level)

As per given , we have

[tex]\sigma=11.8\text{ ounces}[/tex]

[tex]\overline{x}=51 \text{ ounces}[/tex]

n= 44

Significance level for 95% confidence = [tex]\alpha=1-0.95=0.05[/tex]

Using z-value table ,

Two-tailed Critical z-value : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]

Now, the 95% confidence interval for the true population mean textbook weight will be :-

[tex]51\pm (1.96)\dfrac{11.8}{\sqrt{44}}\\\\=51\pm(1.96)(1.7789)\\\\=51\pm3.486644\approx51\pm3.49\\\\=(51-3.49,\ 51+3.49)\\\\=(47.51,\ 54.49) [/tex]

Hence, the 95% confidence interval for the true population mean textbook weight. :  (47.51, 54.49)

To solve the question, we find the specific terms of the sequence using the given formula and illustrate that the difference between any two consecutive terms of this sequence is consistently 4, displaying the sequence's linear progression.

The question requires us to first find the terms t1, t2, t3, and tn+1 of a sequence described by the formula tn = 4n - 1, and then to find the difference tn+1 - tn in its simplest form. To solve this problem, we substitute the appropriate values of n into the given formula and simplify.

To find the difference tn+1 - tn in its simplest form, we subtract tn from tn+1:

tn+1 - tn = (4n + 3) - (4n - 1) = 4

The difference between any two consecutive terms in this sequence is 4. This reveals a consistent increment pattern in the sequence, illustrating its linear nature.

Answer:

there is no question

but it grew 7500

over the time

Step-by-step explanation:

Question:

The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 23700.

(a) Find a function that models the population (t) years after 2000 ( t=0 for 2000).

(b) Use the function from part (a) to estimate the fox population in the year 2008.  

Answer:

A: P(t)=23700e^(.04t)

B: ≈32638

Step-by-step explanation:

A: The formula A=Pe^(rt) can be used. Initial value of 23700, e is the exponential constant, the rate is 4% which can be seen as 4/100, and t=time

B: Use the equation you created and substitute 8 for t since the years of difference between 2008-2000 is 8 years

23700e^(.04(8)) ≈ 32637.9280148

Rounded to the nearest fox is ≈32638

Answer:

4 to 34

Step-by-step explanation:

Answer:

There are a few correct equivalents to this. Please mark brainliest!!!

Step-by-step explanation:

4:34, 6:51, 8:68, and 10;85

Answer:

What do Americans think about preferential hiring of women? Has there been a change in the past decade? In 2000(group 1) and 2010(Group 2), the General Social Survey asked participants if they would favor or oppose preferential hiring of women. In 2000, out of 849 respondents, 271 said yes. In 2010, out of 696 respondents, 225 said yes. The 95% confidence interval for p1-p2 is (-0.0509, 0.04273). What would be an appropriate conclusion? O We are 95% confident that the population proportion in 2010 that supported preferential hiring of women is about 0.0509 and the population proportion in 2000 is 0.04723. We are 95% confident that the pulation proportion in 2000 that supported preferential hiring of women is about 0.0509 and the population proportion in 2010 is 0.04723. We are 95% confidence that the population proportion in 2010 that supported preferential hiring of women is between 0.0509 less to 0.04273 more than the population proportion in 2000. O We are 95% confidence that the population proportion in 2000 that supported preferential hiring of women is between 0.0509 less to 0.04273 more than the population proportion in 2010.

Step-by-step explanation:

Answer:

y+19

Step-by-step explanation:

simply because when it says "more than" or "less than" you have to flip it so it wouldnt be 19+y.

Answer:

At least  one of the events A and B occurs:

(a) 0.5

(b) 0.44

All of the events A, B, C occur:

(a) 0.024

(b) 0

Step-by-step explanation:

Given:

P(A) = 0.2, P(B) = 0.3, P(C) = 0.4

At least  one of the events A and B occurs:

(a) If A and B are mutually exclusive events, then their intersection is 0.

Probability of at least one of them occurring means either of the two occurs or the union of the two events. Therefore,

[tex]P(A\ or\ B)=P(A)+P(B)-P(A\cap B)\\P(A\ or\ B)=0.2+0.3-0=0.5[/tex]

(b) If A and B are independent events, then their intersection is equal to the product of their individual probabilities. Therefore,

[tex]P(A\ or\ B)=P(A)+P(B)-P(A\cap B)\\P(A\ or\ B)=P(A)+P(B)+P(A)P(B)\\P(A\ or\ B)=0.2+0.3-(0.2)(0.3)=0.5-0.06=0.44[/tex]

All of the events A, B, C occur together:

(a) All of the events occurring together means the intersection of all the events.

If A, B, and C are independent events, then their intersection is equal to the product of their individual probabilities. Therefore,

[tex]P(A\cap B\cap C)=P(A)\cdot P(B)\cdot P(C)\\P(A\cap B\cap C)=0.2\times 0.3\times 0.4=0.024[/tex]

(b) If A, B, and C are mutually exclusive events means events A, B, and C can't happen at the same time. Therefore, their intersection is 0.

[tex]P(A\cap B\cap\ C)=0[/tex]

Probability that at least one of the events A and B occurs:

(a) When A and B are mutually exclusive: 0.5 (b) When A and B are independent: 0.44

Probability that all of the events A, B, and C occur:

(a) When A, B, and C are independent: 0.024 (b) When A, B, and C are mutually exclusive: 0

To solve these probability questions, let's understand the given information and the rules of probability related to mutually exclusive and independent events.

Let P(A) = 0.2, P(B) = 0.3, and P(C) = 0.4.

1. Finding the probability that at least one of the events A and B occurs:

(a) When A and B are mutually exclusive:

Mutually exclusive events mean that A and B cannot occur at the same time. Therefore, the probability that at least one of them occurs is given by:

P(A OR B) = P(A) + P(B)

So, P(A OR B) = 0.2 + 0.3 = 0.5

(b) When A and B are independent:

Independent events mean that the occurrence of one event does not affect the occurrence of the other. The probability that at least one of them occurs is given by:

P(A OR B) = P(A) + P(B) - P(A AND B)

For independent events, P(A AND B) is calculated as: P(A AND B) = P(A) × P(B)

So, P(A AND B) = 0.2 × 0.3 = 0.06

Therefore, P(A OR B) = 0.2 + 0.3 - 0.06 = 0.44

2. Finding the probability that all of the events A, B, and C occur:

(a) When A, B, and C are independent:

For independent events, the probability that all of them occur is given by:

P(A AND B AND C) = P(A) × P(B) × P(C)

So, P(A AND B AND C) = 0.2 × 0.3 × 0.4 = 0.024

(b) When A, B, and C are mutually exclusive:

If events are mutually exclusive, it means they cannot all occur together. Therefore, the probability that all of them occur is:

P(A AND B AND C) = 0

Answer:

(a) and (b) see pictures attached

(c) V = 16/35

Step-by-step explanation:

(a) Sketch the base of S in the xy-plane.

See picture 1 attached

(b) Sketch a three-dimensional picture of S with the xy-plane as the floor.

See picture 2 attached

(c) Compute the volume of S.

The volume is given by the triple integral

[tex]\displaystyle\iiint_{S}zdzdydx[/tex]

The cross-sections perpendicular to the x-axis are squares so  

[tex]z=1-x^2[/tex]

The region S is given by the following inequalities

[tex]0\leq x\leq 1\\\\x^2\leq y\leq 1\\\\0\leq z\leq 1-x^2[/tex]

Therefore

[tex]\displaystyle\iiint_{S}zdzdydx=\displaystyle\int_{0}^{1} \displaystyle\int_{x^2}^{1} \displaystyle\int_{0}^{1-x^2} (1-x^2)dzdydx=\\\\\displaystyle\int_{0}^{1}(1-x^2)(1-x^2)(1-x^2)dx=\displaystyle\int_{0}^{1}(1-x^2)^3dx=\displaystyle\frac{16}{35}[/tex]

So the volume V of the solid S is

V=16/35

Answer:

Null hypothesis:[tex]\mu \geq 7.3[/tex]    

Alternative hypothesis:[tex]\mu < 7.3[/tex]    

[tex]z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235[/tex]    

[tex]p_v =P(z<-1.235)=0.1084[/tex]    

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.  

Step-by-step explanation:

1) Data given and notation    

[tex]\bar X=7.2[/tex] represent the sample mean    

[tex]\sigma=0.81[/tex] represent the population standard deviation    

[tex]n=100[/tex] sample size    

[tex]\mu_o =7.3[/tex] represent the value that we want to test    

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)    

[tex]p_v[/tex] represent the p value for the test (variable of interest)    

2) State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :    

Null hypothesis:[tex]\mu \geq 7.3[/tex]    

Alternative hypothesis:[tex]\mu < 7.3[/tex]    

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:    

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)    

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

3) Calculate the statistic    

We can replace in formula (1) the info given like this:    

[tex]z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235[/tex]    

4) P-value    

Since is a one-side lower test the p value would given by:    

[tex]p_v =P(z<-1.235)=0.1084[/tex]    

5) Conclusion    

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.  

Answer:

0.4038

Step-by-step explanation:

Let A and B be the events

A: “The die is fair”

B: “The die lands on 6 two times out of 6”

We want to determine if the die is fair given that it landed on 6 two times out of 6 tosses, that is P(A | B).

By the Bayes' theorem  

[tex]\large P(A|B)=\displaystyle\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^c)P(A^c)}[/tex]

Where [tex]\large A^c[/tex] is the event “the die is not fair”.

Since there are 2 dice,

[tex]\large P(A)=P(A^c)=1/2[/tex]

If the die is fair P(B | A) is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 1/6 and six repeated trials  

[tex]\large P(B|A)=\binom{6}{2}(1/6)^2(5/6)^4=0.2009[/tex]

and [tex]\large P(B|A^c)[/tex] is the probability of getting exactly two six in a binomial experiment with probability of “success” (land on 6) 0.25 and six repeated trials  

[tex]\large P(B|A^c)=\binom{6}{2}(0.25)^2(0.75)^4=0.2966[/tex]

hence

[tex]\large P(A|B)=\displaystyle\frac{0.2009*0.5}{0.2009*0.5+0.2966*0.5}=0.4038[/tex]

To find the probability that the chosen die is fair after rolling 4, 3, 6, 6, 5, 5, we use Bayes' theorem and consider the probability of obtaining this sequence with both a fair die and a biased die. We incorporate the prior probability of choosing any die, which is equal, and compute the probability by dividing the product of the probability for the fair die and its prior probability by the sum of both scenarios' probabilities.

We are asked to determine the probability that the die chosen is the fair die after rolling it six times to obtain the values 4, 3, 6, 6, 5, 5. This problem serves as an application of Bayes' theorem and involves calculating the likelihood of obtaining the observed sequence of rolls under two hypotheses: the die is fair, and the die is biased.

For the fair die, the probability of rolling 4, 3, 6, 6, 5, or 5 is
(1/6) for each, as outcomes are equally likely. Therefore, the probability of rolling 4, 3, 6, 6, 5, 5 with the fair die is (1/6)^6.

Conversely, for the biased die, the probabilities are different. It is 0.15 for rolling 4 or 3 and 0.25 for rolling a 6, while it remains 0.15 for a 5. Thus, the probability of rolling 4, 3, 6, 6, 5, 5 with the biased die is (0.15)^2 * (0.25)^2 * (0.15)^2.

By applying Bayes' theorem, we can update our beliefs about whether the fair die was chosen based on the evidence provided by the rolls. The calculation requires the prior probabilities of choosing each die (which is 1/2 since the die is chosen at random) and the likelihood of the observed sequence under each die. The final probability is a fraction with the numerator being the product of the likelihood of the sequence for the fair die and the prior probability of the fair die, and the denominator is the sum of the probabilities for both scenarios (fair and biased dice).

The exact arithmetic is left as an exercise, as the question was not looking for the numerical solution but rather the approach to finding the answer.

Answer: The margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.

Step-by-step explanation:

Since we have given that

Sample size = 400

Mean = $357.75

Standard deviation = $37.89

At 95% confidence level, z = 1.96

We first find the margin of error.

Margin of error is given by

[tex]z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1.96\times \dfrac{37.89}{\sqrt{400}}\\\\=3.71[/tex]

95% confidence interval would be

[tex]\bar{x}\pm \text{margin of error}\\\\=357.75\pm 3.71\\\\=(357.75-3.71,357.75+3.71)\\\\=(354.04,361.46)[/tex]

Hence, the margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.

Final answer:

The margin of error for a 95% confidence interval of the population mean cost of textbooks is approximately $3.71, resulting in a confidence interval of ($354.04, $361.46). This indicates a 95% level of confidence that the true average cost of textbooks lies within this range.

Explanation:

To calculate the margin of error for the 95% confidence interval for the population mean, we use the formula for margin of error (ME): ME = z * (s/√n), where z is the z-score corresponding to the confidence level, s is the sample standard deviation, and n is the sample size. Given that the student sample size is 400, the sample mean cost is $357.75, and the sample standard deviation is $37.89, we first find the z-score for a 95% confidence level, which is approximately 1.96. We then compute the margin of error.

Margin of Error calculation:
ME = 1.96 * ($37.89/√400) = $1.96 * ($37.89/20) = $1.96 * 1.8945 ≈ $3.71

Now that we have the margin of error, we can calculate the 95% confidence interval for the population mean, which is the range where we expect the true population mean to lie. The confidence interval is: ($357.75 - ME, $357.75 + ME), or ($357.75 - $3.71, $357.75 + $3.71), giving us ($354.04, $361.46). This means that we are 95% confident that the true average cost of textbooks during the first semester in college is between $354.04 and $361.46.

Final answer:

The height of the tree is determined by the angles of elevation and the distance between points A and B on the ground. Given the 45° and 30° angles of elevation and knowing that the horizontal distance AB is 100 feet, we can infer that the tree height is also 100 feet.

Explanation:

To solve for the height of the tree, we can use the trigonometric properties of right triangles and the given angles of elevation. Since the angles of elevation from points A and B to the top of the tree T are 45° and 30° respectively, and the horizontal distance between A and B is 100 feet, we know that we have two separate right triangles with angle T being the top of the tree and O being the base of the tree. We also have an angle of 60° for ∠AOB which will help us determine the distances OA and OB.

Using the 45° angle from point A, we have a 45°-45°-90° triangle, which means the height of the tree (OT) is equal to OA, the distance from the base of the tree to point A. From point B with a 30° angle, we have a 30°-60°-90° triangle. In a 30°-60°-90° triangle, the height (OT) would be √3 times smaller than the distance OB (the longer side).

Since ∠AOB is 60° we know that triangle AOB is equilateral. Therefore, distances OA and OB are both 100 feet. Now we just need to calculate the height OT in one of the triangles. Taking the 45° triangle, we have OT = OA = 100 feet. Thus, the height of the tree T is 100 feet.

Final answer:

The height of the tree can be determined by using right triangle trigonometry involving the angles of elevation from two points on the ground and the known distance between them. Mathematically, the height of the tree is found to be approximately 28.87 feet.

Explanation:

To determine the height of the tree, we use the provided angles of elevation from points A and B and the distance between these points. The tree, points A and B, and the angles form two right triangles, one with a 45° angle of elevation and the other with a 30° angle of elevation. Since the angle of elevation from point A is 45°, we know that for a 45° right-angled triangle, the tangent is 1, which means that the opposite side (height of the tree) is equal to the adjacent side (distance from A to O).

First, we can calculate the distance from A to O using the angle of 60° between points A and O given as ∠AOB. The distance AO is half of AB because ∠AOB is an equilateral triangle's angle so AO = 50 feet. Next, using the fact that the tan 30° from point B is equal to the height of the tree divided by the distance from B to O, we can calculate the height. Since the distance from A to O is 50 feet, the distance from B to O is also 50 feet. The tangent of 30° is 1/√3, so the tree's height (H) is equal to 50 feet times tan 30°, which is approximately 28.87 feet.

Answer:

The 95% confidence interval would be given by (12.03;14.37)    

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=13.2[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)

s=18.9 represent the sample standard deviation

n=997 represent the sample size  

2) Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=997-1=996[/tex]

Since the confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,996)".And we see that [tex]t_{\alpha/2}=1.96[/tex] and this value is exactly the same for the normal standard distribution and makes sense since the sample size is large enough to approximate the t distribution with the normal standard distribution.

Now we have everything in order to replace into formula (1):

[tex]13.2-1.96\frac{18.9}{\sqrt{997}}=12.03[/tex]    

[tex]13.2+1.96\frac{18.9}{\sqrt{997}}=14.37[/tex]

So on this case the 95% confidence interval would be given by (12.03;14.37)    

Answer:

A. TYPE 1 ERROR only

Step-by-step explanation:

In general terms:

‘a hypothesis has been rejected when it should have been accepted’. When this occurs, it is called a type I error, and,

‘a hypothesis has been accepted when it should have been rejected’.

When this occurs, it is called a type II error,

When testing a hypothesis, the largest value of probability which is acceptable for a type I error is called the level of significance of the test. The level of significance is indicated by the symbol α (alpha) and the levels commonly adopted are 0.1,0.05,0.01, 0.005 and 0.002.

A level of significance of 1%,say,0.01 means that 1 times in 100 the hypothesis has been rejected when it should have been accepted.

In significance tests, the following terminology is frequently adopted:

(i) if the level of significance is 0.01 or less, i.e. the confidence level is 9 9% or more, the results are considered to be highly significant, i.e. the results are considered likely to be correct,

(ii) if the level of significance is 0.05 or between 0.05and0.01,i.e.theconfidencelevelis95%or between 95% and 99%, the results are considered to be probably significant, i.e. the results are probably correct,

(iii) if the level of significance is greater than 0.05, i.e. the confidence level is less than 95%, the results are considered to be not significant, that is, there are doubts about the correctness of the results obtained.