Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J.When all other things remain the same, which of the following describes the relationship between the two confidence intervals?a)The width of i400 will be 4 times the width of i100.b) The width of i400 will be 2 times the width of i100c)The width of i400 will be equal to the width of i100.d)The width of I400 will be 1/2 times the width of I100e)The width of I400 will be 1/4 times the width of I100.

Answer:

Correlation coefficient 'r' would be lower.

Step-by-step explanation:

Correlation is co movement relationship between two variables.

Correlation coefficient 'r' is positive, when variables move in same direction. 'r' is negative when variables move in opposite direction. So, 'r' lies between -1 (perfect negative correlation) & +1 (perfect positive correlation). High 'r' magnitude reflects strong correlation between the variables, Low 'r' reflects  weak weak correlation between the variables.

Correlation studied between amount of daily exercise and weight  : It is negative as exercise & weight are negatively correlated - more exercise, less weight & less exercise, more weight. 'r' is given = -0.21

If sample is restricted to people weighing less than 180 pounds : It would lead to fall in 'r'. Such because these low weight people are likely to have good natural metabolic rate, naturally slim body physique / figure. So, in their case, exercise & body weight are likely to be less (weakly) correlated than normal case.

Answer:

(a) The test statistic value is, 5.382.

(b) Retain the null hypothesis.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

The information provided is:

Observed values:

Half Pint: 36

XXX: 35

Dark Night: 9

TOTAL: 80

The expected proportions are:

Half Pint: 40%

XXX: 40%

Dark Night: 20%

Compute the expected values as follows:

E (Half Pint) [tex]=\frac{40}{100}\times 80=32[/tex]

E (XXX) [tex]=\frac{40}{100}\times 80=32[/tex]

E (Dark night) [tex]=\frac{20}{100}\times 80=16[/tex]

Compute the test statistic as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

    [tex]=[\frac{(36-32)^{2}}{32}]+[\frac{(35-32)^{2}}{32}]+[\frac{(9-16)^{2}}{16}][/tex]

    [tex]=3.844[/tex]

The test statistic value is, 5.382.

The degrees of freedom of the test is:

n - 1 = 3 - 1 = 2

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.1463

*Use a Ch-square table.

p-value = 0.1463 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Thus, concluding that the production of the premium lagers matches these consumer preferences.

Answer:

a)Null hypothesis:[tex]p\leq 0.14[/tex]  

Alternative hypothesis:[tex]p > 0.14[/tex]  

b) For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

[tex]z_{crit} = 2.33[/tex]

So then the rejection region would be [tex](2.33 , \infty)[/tex]

c) The significance level provided [tex]\alpha=0.01[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.52)=0.006[/tex]  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

Step-by-step explanation:

Data given and notation

n=590 represent the random sample taken

X=104 represent the drivers were wearing their seat belts

We can estimate the sample proportion like this:

[tex]\hat p=\frac{104}{590}=0.176[/tex] estimated proportion of  drivers were wearing their seat belts

[tex]p_o=0.14[/tex] is the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

a) System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of drivers were wearing their seat belts is higher than 0.14 or no, so the system of hypothesis are.:  

Null hypothesis:[tex]p\leq 0.14[/tex]  

Alternative hypothesis:[tex]p > 0.14[/tex]  

Part b

For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

[tex]z_{crit} = 2.33[/tex]

So then the rejection region would be [tex](2.33 , \infty)[/tex]

Part c

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.176 -0.14}{\sqrt{\frac{0.14(1-0.14)}{590}}}=2.52[/tex]  

Statistical decision  

The significance level provided [tex]\alpha=0.01[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.52)=0.006[/tex]  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

Answer:

See explanation

Step-by-step explanation:

Solution:-

- Let the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law = p.

- A claim was made that p = 0.14. We will state our hypothesis:

                Null hypothesis: p = 0.14

- Two months after the campaign, y = 104 out of a random sample of n = 590 drivers were wearing their seat belts. The sample proportion can be determined as:

               Sample proportion ( p^ ) = y / n = 104 / 590 = 0.176

- The alternate hypothesis will be defined by a population proportion that supports an increase. So we state the hypothesis:

               Alternate hypothesis: p > 0.14

- The rejection is defined by the significance level ( α = 0.01 ). The rejection region is defined by upper tail of standard normal.

- The Z-critical value that limits the rejection region is defined as:

                            P ( Z < Z-critical ) = 1 - 0.01 = 0.99

                            Z-critical = 2.33

- All values over Z-critical are rejected.

- Determine the test statistics by first determining the population standard deviation ( σ ):

- Estimate σ using the given formula:

                      σ = [tex]\sqrt{\frac{p*(1-p)}{n} } = \sqrt{\frac{0.14*(1-0.14)}{590} }= 0.01428[/tex]

- The Z-test statistics is now evaluated:

                     Z-test = ( p^ - p ) / σ

                     Z-test = ( 0.1763 - 0.14 ) / 0.01428

                    Z-test = 2.542

- The Z-test is compared whether it lies in the list of values from rejection region.

                     2.542 > 2.33

                     Z-test > Z-critical

Hence,

                     Null hypothesis is rejected

- The claim made over the effectiveness of campaign is statistically correct.

Answer:

The platform cannot hold both elephants.

Step-by-step explanation:

This problem is solved by conversion of units.

Elephant A weighs 11,028 pounds

Elephant B weighs 5 1/2 = 5.5 tons

The platform can hold 22,000 pounds

To see if the platform holds both elephants, the first step is converting the weigth of Elephant B to pounds.

Each ton has 2000 pounds.

So 5.5 tons have 5.5*2000 = 11000 pounds.

So Elephant B weighs 11000 pounds

Combined weights of Elephants A and B

11,028 + 11,000 = 22,028 > 22,000

The platform cannot hold both elephants.

Answer:

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 40, p = 0.2[/tex]

So

[tex]\mu = E(X) = np = 40*0.2 = 8[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40*0.2*0.8} = 2.53[/tex]

What is the probability that a randomly selected bag of this size has 10 or more green candies

Using continuity correction, this is [tex]P(X \geq 10 - 0.5) = P(X \geq 9.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 9.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 8}{2.53}[/tex]

[tex]Z = 0.59[/tex]

[tex]Z = 0.59[/tex] has a pvalue of 0.7224

1 - 0.7224 = 0.2776

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Answer:

[tex]P(x\geq 10)=0.2682[/tex]

Step-by-step explanation:

The number x of green candies in a bag of 40 candies follows a binomial distribution, because we have:

So, the probability that in a bag of 40 candies, x are green is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Replacing, n by 40 and p by 0.2, we get:

[tex]P(x)=\frac{40!}{x!(40-x)!}*0.2^{x}*(1-0.2)^{40-x}[/tex]

So, the probability that a randomly selected bag of this size has 10 or more green candies is equal to:

[tex]P(x\geq 10)=P(10)+P(11)+...+P(40)\\P(x\geq 10)=1-P(x<10)[/tex]

Where [tex]P(x<10)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)[/tex]

So, we can calculated P(0) and P(1) as:

[tex]P(0)=\frac{40!}{0!(40-0)!}*0.2^{0}*(1-0.2)^{40-0}=0.00013\\P(1)=\frac{40!}{1!(40-1)!}*0.2^{1}*(1-0.2)^{40-1}=0.00133[/tex]

At the same way, we can calculated P(2), P(3), P(4), P(5), P(6), P(7), P(8) and P(9) and get that P(x<10) is equal to:

[tex]P(x<10)=0.7318[/tex]

Finally, the probability [tex]P(x\geq 10)[/tex] that a randomly selected bag of this size has 10 or more green candies is:

[tex]P(x\geq 10)=1-P(x<10)\\P(x\geq 10)=1-0.7318\\P(x\geq 10)=0.2682[/tex]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                          P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students received a passing grade = 77%

           n = sample of tests = 40

           p = population proportion

Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                           level of significance are -2.5758 & 2.5758}  

P(-2.5758 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.5758) = 0.99

P( [tex]-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [[tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

 = [ [tex]0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] , [tex]0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] ]

 = [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

Answer:

Step-by-step explanation:

Z=-1.5

-1.5=2.5

Final answer:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, subtract the area to the left of z = -1.5 from the area to the left of z = 2.5 to be 0.927.

Explanation:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we can subtract the area to the left of z = -1.5 from the area to the left of z = 2.5.

Using the z-table, we can find that the area to the left of z = -1.5 is approximately 0.0668 and the area to the left of z = 2.5 is approximately 0.9938.

Therefore, the area between z = -1.5 and z = 2.5 is approximately 0.9938 - 0.0668 = 0.927.

The expected number of tests using the group testing procedure is 1.75.

To find the expected number of tests using the group testing procedure, we need to consider the different possible outcomes. Let's break it down:

If no one has the disease (probability = 1 - p), then only one test is required.

If at least one individual has the disease (probability = p), the test on the combined sample will yield a positive result, and then the n individual tests will be carried out.

Therefore, the expected number of tests is:

Expected number of tests = (probability of no disease) * (number of tests in this case) + (probability of disease) * (number of tests in this case)

For the first case, the number of tests is 1.

For the second case, the number of tests is n + 1, because one additional test is required after the positive result from the combined sample.

Substituting the values, Expected number of tests = (1 - p) * 1 + p * (n + 1)

Given p = 0.15 and n = 5, substituting the values we get:

Expected number of tests = (1 - 0.15) * 1 + 0.15 * (5 + 1) = 0.85 * 1 + 0.15 * 6 = 0.85 + 0.9 = 1.75

Therefore, the expected number of tests using this procedure is 1.75.

Answer:

choice a....625 = [tex]5^{4}[/tex] in exponential form

Step-by-step explanation:

625 = 25*25 =  [tex]25^{2}[/tex]  =  [tex]5^{4}[/tex]

Answer:

choice A well be correct !! (did it on usa test prep)

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Two tangents to the circle (until the point where the tangent and circle touch) has the same length, therefore, AR=AT, RG=GE, EN=NT

Then just add up everything!

The cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.

To solve this problem, we can use the following steps:

Define the variables.

Let x be the number of cars rented per day and y be the rate per day.

Write down the equation for the revenue.

The revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the equation for the revenue is:

R = x * y

Write down the equation for the decrease in demand. For each $1 increase in rate, 10 fewer cars are rented. Therefore, the equation for the decrease in demand is:

D = -10 * (y - 30)

Set the revenue equal to the maximum value. The revenue is maximized when the derivative of the revenue function is zero. Therefore, we set the derivative of the revenue function equal to zero and solve for y.

R' = x = 0

x = 440

y = 30

Calculate the maximum revenue. The maximum revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the maximum revenue is:

R = 440 * 30 = $13200

Therefore, the cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.

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Answer:

There is no relationship between voles and food preference (The food preferences among vole species are independent of one another)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. The null hypothesis tries to establish that the old theory is true. So, for the case above, the old theory is that there is no relationship between voles species and food preference which is the null hypothesis.

The null hypothesis in Dr. Pagels' study is that there is no difference in the food preferences for peanut butter-oatmeal mixture and apple slices between meadow and common voles.

In the study conducted by Dr. Pagels for determining the food preference of meadow and common voles, the null hypothesis posits that there is no difference in preference for the peanut butter-oatmeal mixture or apple slices between the two species of voles. This implies that both meadow and common voles would choose either food option at an equal rate, suggesting that any observed preference could be attributed to random chance rather than a true preference.

The purpose of the null hypothesis is to establish a baseline expectation that no effect or difference is present, which can then be challenged by the experimental data. If significant differences in the vole populations' food choices are observed, the null hypothesis may be rejected, pointing to a potential preference for one food type over the other among the different vole species.

Answer:12.57

Step-by-step explanation:

Answer:

12.566370614359 rounded to the nearest hundreth is 12.57

Answer:

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.  

Step-by-step explanation:

Let's find out how many days in total Guido stayed in US in these 3 years 2017, 2018 and 2019.

Year = 2017

Days = 200

Year = 2018

Days = 180

Year = 2019

Days = 70

Total days stayed = 200 + 180 + 70

Total Days Stayed = 450 days.

In U.S, there are two tests are in place and for non-citizen of U.S and for the resident Alien or non - resident Alien status, one must pass one of these two tests, which are as follows:

1. Green Card Test:

2. Substantial Presence Test:

Here, in this problem, Guido is citizen and resident of Belgium. So, will check his criteria according to the substantial presence test.

So, the question is: how many days Guido was present in the U.S in 2018 under resident alien status.

In 2018, Guido stayed in US for 180 days.

So, according to the Substantial Presence test, one must be physically present in US for more than 31 days to be eligible for resident alien status. In addition, in 2018, his total of physical presence in US in 2018 and one third of physical presence in 2017 must be greater than 183 days.

If we see, both conditions are matched in case of Guido.

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.  

Final answer:

In 2018, Guido was present in the United States for a total of 180 days according to the substantial presence test for determining resident alien status for tax purposes.

Explanation:

Under the substantial presence test, which is used to determine if an individual is a resident alien for tax purposes in the United States, only the days present in the current year (which, in the scenario provided, is 2018) are counted in full. In this case, Guido was present in the U.S. for 180 days in 2018. Days from prior years are counted partially, with only 1/3 of the days in the first preceding year and 1/6 of the days from the second preceding year included in the calculation. However, when determining how many days were present in a given year, such as 2018 in this example, only the days in that specific year are relevant. Therefore, according to the substantial presence test, in 2018, Guido was present in the United States for a total of 180 days.

Answer:

Approximately = 20.0 inch to the nearest tenth

Step-by-step explanation:

We are going to calculate this by using the formula of the circle in a way.

Radius = 6 inches

Now between 10:25 a.m. and 11:00 a.m , the minute hand moved 35 minutes.

But there are total of 60 minutes in the clock which makes it a complete circle.

So 60 minutes = 2π

35 minutes = ?.

35 minutes =( 35*2π)/60

35 minutes = 1.166667π

So the distance covered by the minute hand = 1.166667π * 6 inches

= 21.991 inches

Approximately = 20.0 inch to the nearest tenth

Answer:5/3 jars left

Step-by-step explanation:

Convert the total number of jars to improper fraction from mixed fraction

The subtract the total number of jars from the total number of empty jars

16/3 -11/3

5/3

Step-by-step explanation:

A bag contains 23 coins, some dimes and some quarters. The total amount of money in the bag is $2.75.

Let d be the  number of dimes

and q be the number of quarters

Total cons = 23

so equation becomes

[tex]d+q= 23\\[/tex]

[tex]q=23-d[/tex]

1 dime = 10 cents

and 1 quarter =25 cents

The total amount of money in the bag is $2.75

2.75= 275 cents

[tex]10d+25q=275[/tex]

solve the equation for d  and q

Plug in [tex]q=23-d[/tex] for q in second equation

[tex]10d+25q=275\\10d+25(23-d)=275\\10d+575-25d=275\\[/tex]

combine like terms and subtract 575 from both sides

[tex]10d+575-25d=275\\-15d=275-575\\-15d=-300\\[/tex]

divide both sides by -15

d=20

so the number of dimes = 20

[tex]q=23-d\\q=23-20\\q=3[/tex]

Number of quarter = 3

Answer:

20 dimes

3 quarters

Answer: 21 quarts. Annie will need a total of 21 quarts of coffee.

Step-by-step explanation: 16 fl oz = 0.5 quarts. 0.5 * 42 =21

21 quartz of coffee needed to 42 mugs.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Capacity of Coffee mug= 16 fluid ounce

1 fluid ounce = 0.03125 liquid quartz

16 fluid ounce = 16 x 0.03125

                       = 0.5 quartz

So, for 42 mugs the amount coffee needed

= 42 x 0.5

= 21 quartz

Hence, 21 quartz of coffee needed to 42 mugs.

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Answer:

Correct option: (C) Yes, because the sample sizes are both greater than 30.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

For the first sample, the sample size of the sample selected is:

n₁ = 32 > 30

Ans for the second sample, the sample size of the sample selected is:

n₂ = 41 > 30

Both the samples selected are quite large.

So, the Central limit theorem can be used to approximate the distribution of of the two sample means.

Ans since the distribution of the two sample means follows a normal distribution, the difference of the two means will also follows normal distribution.

Thus, the correct option is (C).

C Yes, because the sample sizes are both greater than 30.

The following information should be considered;

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Answer:

D. 24/7

Step-by-step explanation:

SOH CAH TOA

we doing the tangent so

tan (α) = opposite / adjacent

tan (α) = 24/7

Answer:

Option E) The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.

Step-by-step explanation:

Gallup asked 2100 Japanese, so the sample size is:

n = 2100

67% of the Japanese answered in affirmative. This means the proportion of population which answered in favor or affirmative is:

p = 67%

Based on his findings, Gallup constructed a confidence interval. We have to identify the correct confidence interval i.e. the population percentage of Japanese who believes in the complete recovery of Japan.

The confidence interval will always be in form of a range of values i.e. between two values: A lower limit and an upper limit. This automatically removes choices A and B from the list of correct answers.

Furthermore, the confidence interval is symmetric about the sample proportion(p), as the formula to calculate the confidence interval for a population proportion is:

( p - M.E, p + M.E )

where M.E means Margin of Error. Since, same value(M.E) is added to and subtracted from the sample proportion(p), the confidence interval will be symmetric about the sample proportion.

So, now we will find if the values in choices C,D and E are symmetric about the mean or not. If the values are symmetric the difference of the values in each option from p = 67% must be same.

Choice C)

60% and 70%

We can easily tell that these values are not symmetric about 67%. Therefore, this cannot be the answer.

Choice D)

65.13% and 70.21%

67% - 65.13% = 1.87%

70.21% - 67% = 3.21%

These two values are not symmetric either. So these cannot be our confidence interval.

Choice E)

64.82% and 69.18%

67% - 64.82% = 2.18%

69.18% - 67% = 2.18%

These two values are same distance apart from 67%, this means they are symmetric about the sample proportion. Hence, choice E is the correct confidence interval. The Margin of Error is 2.18%

The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.

Answer:

C. x = 3cm

Step-by-step explanation:

The formula for volume of a triangular prism is

V = base * height

x in this case equals height, and the base is the area of the triangular base, which is

A(triangle) = 1/2 b*h

                 = 1/2 7*10 = 35 square centimeters

Plug this back into our formula:

V = base * height

105 = 35x

Solve for x.

105/35 = x

C. x = 3 cm

Answer:

C. 3 cm

Step-by-step explanation:

The volume of a triangular prism is denoted by: [tex]V=Bh[/tex], where B is the base area and h is the height.

Here, the base is actually the triangle, and we can calculate this area by using the formula for a triangle's area: [tex]A=\frac{1}{2} bh[/tex]. Here, b = 10 and h = 7, so:

[tex]A=\frac{1}{2} bh[/tex]

[tex]A=\frac{1}{2} *10*7=5*7=35[/tex] cm squared

Now, the height of the prism is x and we already know the volume is 105, so plug these values in:

[tex]V=Bh[/tex]

[tex]105=35*x[/tex]

x = 105/35 = 3

The answer is C.

Answer:

D) 4

Step-by-step explanation:

4x + 24 = 8x + 2x

adding like terms

4x + 24 = 10x

isolate x now

4x+24-4x = 10-4x

24 = 6x

24/6 = 6x/6

4 = x

D) 4

check our answer by plugging solution into equation

4(4) + 24 = 8(4) + 2(4)

16 + 24 = 32 + 8

40 = 40

Answer:

-8/7

Step-by-step explanation:

Answer:

  for independent A and B, P(A|B) = P(A)

Step-by-step explanation:

The definition of  conditional probability is ...

  P(A|B) = P(A&B)/P(B)

When A and B are independent, ...

  P(A&B) = P(A)·P(B)

so the conditional probability is ...

  P(A|B) = (P(A)·P(B))/P(B) = P(A) . . . . . for independent A and B

In words, when A and B are independent, the probability of A given B is the same as the probability of A. That is, the probability of B has no effect on the probability of A.

Answer:

Option D, 72 cubic inches

Step-by-step explanation:

The formula for the volume of a rectangular prism is length*width*height, which in this case is 3*3*8=72 cubic inches, or option D. Hope this helps!

Answer: D) 72

Step-by-step explanation: To get the volume of the rectangular prism all you got do is multiply the width x length x height. Therefore:

3 x 3 x 8 = 72

The answer is D) 72

(Hope this helps)

Answer:

d = 2

Step-by-step explanation:

We have four unknown numbers a, b, c, d

It is given that the mode is 3,

Since the mode is 3 then at least two numbers are 3.

It is given that the median is 3,

Since the median is 3 which means the middle two values must be 3

a, 3, 3, d

It is given that the mean of the four numbers is 4,

Since the mean of the four number is 4 then

mean = (a + 3 + 3 + d)/4

4 = (a + 6 + d)/4

4*4 = a + 6 + d

16 = a + 6 + d    eq. 1

It is given that the range is 6,

Since the range is 6 which is the difference between highest and lowest number that is

a - d = 6

a = 6 + d    eq. 2

Substitute the eq. 2 into eq. 1

16 = a + 6 + d

16 = (6 + d) + 6 + d

16 = 12 + 2d

2d = 16 - 12

d = 4/2

d = 2

Substitute the value of d into eq. 2

a = 6 + d

a = 6 + 2

a = 8

so

a, b, c, d = 8, 3, 3, 2

Verification:

a ≤ b ≤ c ≤ d

8 ≤ 3 ≤ 3 ≤ 2

mean = (a + b + c + d)/4

mean = (8 + 3 + 3 + 2)/4

mean = 16/4

mean = 4

range = a - d

range = 8 - 2

range = 6

The 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't is approximately  16.6  to  32.4  ng/mL.

To find the 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't, we can use the formula for the confidence interval for the difference between two means:

[tex]\[ \text{CI} = (\bar{X}_1 - \bar{X}_2) \pm Z \times \sqrt{\frac{{S_1^2}}{{n_1}} + \frac{{S_2^2}}{{n_2}}} \][/tex]

Where:

[tex]\( \bar{X}_1 \) and \( \bar{X}_2 \)[/tex] are the sample means of the two groups.

[tex]\( S_1 \) and \( S_2 \)[/tex] are the sample standard deviations of the two groups.

[tex]\( n_1 \) and \( n_2 \)[/tex] are the sample sizes of the two groups.

Z is the critical value from the standard normal distribution for the desired confidence level.

Given:

[tex]\( \bar{X}_1 = 83.6 \)[/tex] (mean concentration of DEHP for people who have eaten fast food)

[tex]\( S_1 = 194.7 \)[/tex] (standard deviation of DEHP for people who have eaten fast food)

[tex]\( n_1 = 3095 \)[/tex] (sample size of people who have eaten fast food)

[tex]\( \bar{X}_2 = 59.1 \)[/tex] (mean concentration of DEHP for people who haven't eaten fast food)

[tex]\( S_2 = 152.1 \)[/tex] (standard deviation of DEHP for people who haven't eaten fast food)

[tex]\( n_2 = 5782 \)[/tex] (sample size of people who haven't eaten fast food)

First, we need to calculate the standard error of the difference in means:

[tex]\[ SE = \sqrt{\frac{{S_1^2}}{{n_1}} + \frac{{S_2^2}}{{n_2}}} \][/tex]

Then, we'll find the critical value Z for a 95% confidence interval, which corresponds to  Z = 1.96  for a two-tailed test.

Finally, we'll plug in the values to calculate the confidence interval.

Let's do the calculations:

First, let's calculate the standard error of the difference in means:

[tex]\[ SE = \sqrt{\frac{{194.7^2}}{{3095}} + \frac{{152.1^2}}{{5782}}} \]\[ SE \approx \sqrt{\frac{{37936.09}}{{3095}} + \frac{{23131.41}}{{5782}}} \]\[ SE \approx \sqrt{12.2604 + 4.0006} \]\[ SE \approx \sqrt{16.261} \]\[ SE \approx 4.032 \][/tex]

Now, we'll find the critical value  Z  for a 95% confidence interval, which corresponds to  Z = 1.96  for a two-tailed test.

Finally, we'll calculate the confidence interval:

[tex]\[ \text{CI} = (83.6 - 59.1) \pm 1.96 \times 4.032 \]\[ \text{CI} = 24.5 \pm 1.96 \times 4.032 \]\[ \text{CI} = 24.5 \pm 7.9072 \][/tex]

Now, let's find the bounds of the confidence interval:

Upper Bound:  24.5 + 7.9072 = 32.4072

Lower Bound:  24.5 - 7.9072 = 16.5928

Rounded to one decimal place, the 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't is approximately  16.6  to  32.4  ng/mL.

Question :

Is Fast Food Messing With Your Hormones? Examine the results of a study investigating whether fast food consumption increases one's concentration of phthalates, an ingredient in plastics which has been linked to multiple health problems including hormone disruption. The study included 8877 people who recorded all the food they ate over a 24-hour period and then provided a urine sample. Two specific phthalate byproducts were measured (in ng/mL) in the urine: DEHP and DiNP. Find a 95% confidence interval for the difference, HlF MN, in mean concentration between people who have eaten fast food in the last 24 hours and those who haven't. The mean concentration of DEHP in the 3095 participants who had eaten fast food was XF = 83.6 with SF = 194.7, while the mean for the 5782 participants who had not eaten fast food was TN = 59.1 with SN = 152.1. Round your answers to one decimal place: The 95% confidence interval is ______ to _________.

The 95% confidence interval is 16.6 ng/mL to 32.4 ng/mL.

To find the 95% confidence interval for the difference in mean concentration of DEHP between people who have eaten fast food in the last 24 hours and those who haven't, we use the formula for the confidence interval of the difference between two means with unequal variances (often referred to as Welch's t-test).

Given:

Mean concentration for fast food consumers [tex](\( \bar{X}_F \))[/tex] = 83.6 ng/mL

- Standard deviation for fast food consumers [tex](\( S_F \))[/tex] = 194.7 ng/mL

- Sample size for fast food consumers [tex](\( n_F \))[/tex] = 3095

- Mean concentration for non-fast food consumers [tex](\( \bar{X}_N \))[/tex] = 59.1 ng/mL

- Standard deviation for non-fast food consumers [tex](\( S_N \))[/tex] = 152.1 ng/mL

- Sample size for non-fast food consumers [tex](\( n_N \))[/tex] = 5782

The formula for the 95% confidence interval for the difference in means [tex](\( \mu_F - \mu_N \))[/tex] is:

[tex]\[ (\bar{X}_F - \bar{X}_N) \pm t^* \sqrt{\frac{S_F^2}{n_F} + \frac{S_N^2}{n_N}} \][/tex]

First, we calculate the standard error (SE):

[tex]\[ SE = \sqrt{\frac{S_F^2}{n_F} + \frac{S_N^2}{n_N}} \][/tex]

Plugging in the values:

[tex]\[ SE = \sqrt{\frac{194.7^2}{3095} + \frac{152.1^2}{5782}} \]\[ SE = \sqrt{\frac{37926.09}{3095} + \frac{23133.41}{5782}} \]\[ SE = \sqrt{12.253 + 4.001} \]\[ SE = \sqrt{16.254} \]\[ SE = 4.03 \][/tex]

Next, we find the degrees of freedom (df) using the formula for Welch's t-test:

[tex]\[ df \approx \frac{\left( \frac{S_F^2}{n_F} + \frac{S_N^2}{n_N} \right)^2}{\frac{\left( \frac{S_F^2}{n_F} \right)^2}{n_F-1} + \frac{\left( \frac{S_N^2}{n_N} \right)^2}{n_N-1}} \]\[ df \approx \frac{\left( 12.253 + 4.001 \right)^2}{\frac{12.253^2}{3094} + \frac{4.001^2}{5781}} \]\[ df \approx \frac{16.254^2}{\frac{150.13}{3094} + \frac{16.008}{5781}} \]\[ df \approx \frac{264.188}{0.0485 + 0.0028} \]\[ df \approx \frac{264.188}{0.0513} \]\[ df \approx 5149 \][/tex]

For a large [tex]\( df \), the \( t^* \)[/tex] value for a 95% confidence interval is approximately 1.96.

Now, we can calculate the confidence interval:

[tex]\[ (\bar{X}_F - \bar{X}_N) \pm t^* \cdot SE \]\[ (83.6 - 59.1) \pm 1.96 \cdot 4.03 \]\[ 24.5 \pm 7.9 \][/tex]

So, the 95% confidence interval for the difference in mean concentration of DEHP between people who have eaten fast food in the last 24 hours and those who haven't is:

[tex]\[ 16.6 \text{ to } 32.4 \][/tex]

The 95% confidence interval is 16.6 to 32.4 ng/mL.

Complete  question- Is Fast Food Messing With Your Hormones? Examine the results of a study investigating whether fast food consumption increases one's concentration of phthalates, an ingredient in plastics which has been linked to multiple health problems including hormone disruption. The study included 8877 people who recorded all the food they ate over a 24-hour period and then provided a urine sample. Two specific phthalate byproducts were measured (in ng/mL) in the urine: DEHP and DiNP. Find a 95% confidence interval for the difference, HlF MN, in mean concentration between people who have eaten fast food in the last 24 hours and those who haven't. The mean concentration of DEHP in the 3095 participants who had eaten fast food was XF = 83.6 with SF = 194.7, while the mean for the 5782 participants who had not eaten fast food was TN = 59.1 with SN = 152.1. Round your answers to one decimal place: The 95% confidence interval is ______ to _________.

Answer: 1.6

Order the numbers

5,6,6,8,10

Add

5+6+6+8+10=35

Divide

35÷5=7

Mean: 7

Sum divided by the count.

Final Answer: 1.6

Answer:

1.6

Step-by-step explanation:

Mean: 5 + 6 + 6 + 8 + 10 = 35/5 = 7

7 - 5 = 2

7 - 6 = 1

7 - 6 = 1

7 - 8 = 1

7 - 10 = 3

1 + 1 + 1 + 2 + 3 = 8/5 = 1.6

Answer:

a)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c)

i) p(x) = s(x+4)

ii) s(x) = p(x-4)

Step-by-step explanation:

Complete Question

Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.

a) Suppose Primo Pizza's profit each day is 1.4 times as large as the profit of Pizza Supreme

i. Write a function formula for p using the function s.

ii. Write a function formula for s using the function p.

b) Suppose Primo Pizza's profit each day is $200 more than the profit of Pizza Supreme.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

c) Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

The profits per day for Primo Pizza, x days after June 1 = p(x)

The profits per day for Supreme Pizza, x days after June 1 = s(x)

a) Primo Pizza's profits per day is 1.4 times that of Supreme Pizza's per day.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b) Primo Pizza profits per day is $200 more than that of Supreme Pizza

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c) Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

Supreme Pizza's profit per day, 4 days later = s(x+4)

So,

i) p(x) = s(x+4)

ii) This means that Supreme Pizza's profit per day is the same as Primo Pizza's profit per day four days ago.

Primo Pizza's profit per day four days ago = p(x-4)

So,

s(x) = p(x-4)

Hope this Helps!!!

Primo Pizza's profit function p(x) is related to Pizza Supreme's profit function s(x) such that p(x) = s(x + 4). Similarly, s(x) = p(x - 4). These functions express the profits in terms of each other with a 4-day shift in time.

Given that Primo Pizza's profit p(x) on a given day is the same as Pizza Supreme's profit s(x) 4 days later, we can write the following relationships between the two functions:

p(x) = s(x + 4)

s(x) = p(x - 4)

This implies that to find Primo Pizza's profit on the x-th day, we need to find out what Pizza Supreme's profit was on the (x + 4)-th day. Conversely, to compute Pizza Supreme's profit on the x-th day, we need to find Primo Pizza's profit 4 days earlier, on the (x - 4)-th day.