The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the claim is false. The advocate surveyed 50 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 11.2 minutes. The standard deviation for this survey group was 3.1 minutes. What can be concluded at the 0.05 level of significance?H0: mu.gif= 10Ha: mu.gif [ Select ] [">", "<", "Not Equal to"] 10Test statistic: [ Select ] ["Chi-square", "F", "Z", "t"] p-Value = [ Select ] ["0.105", "0.009", "0.091", "0.025"] . Round your answer to three decimal places. [ Select ] ["Reject the null hypothesis", "Fail to reject the null hypothesis"] Conclusion: There is [ Select ] ["sufficient", "insufficient"] evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes.

Answer:

Step-by-step explanation:

Answer:

The point estimate for population mean is 8.129 Mpa.

Step-by-step explanation:

We are given the following in the question:

Data on flexural strength(MPa) for concrete beams of a certain type:

11.8, 7.7, 6.5, 6.8, 9.7, 6.8, 7.3, 7.9, 9.7, 8.7, 8.1, 8.5, 6.3, 7.0, 7.3, 7.4, 5.3, 9.0, 8.1, 11.3, 6.3, 7.2, 7.7, 7.8, 11.6, 10.7, 7.0

a) Point estimate of the mean value of strength for the conceptual population of all beams manufactured

We use the sample mean, [tex]\bar{x}[/tex] as the point estimate for population mean.

Formula:

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]\bar{x} = \dfrac{\sum x_i}{n} = \dfrac{219.5}{27} = 8.129[/tex]

Thus, the point estimate for population mean is 8.129 Mpa.

To estimate the mean flexural strength, the sum of strengths (219.5 MPa) is divided by the total number of beams measured (26), which yields a mean value of 8.442 MPa when rounded to three decimal places. The estimator used is the sample mean.

To calculate a point estimate of the mean value for flexural strength (MPa) for a conceptual population of concrete beams, we use the sum of all measured strengths and divide by the number of measurements. The sum of the flexural strengths is provided as Σxi = 219.5 MPa.

Given the dataset:

The number of measurements is the number of data points, which is 26. To find the mean:

mean = Sum of strengths / Number of measurements

mean = 219.5 MPa / 26

mean = 8.442 MPa (rounded to three decimal places)

The estimator used here is the sample mean (×).

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Answer:

15

Step-by-step explanation:

We are given that

Number of alpha protein subunits=4

Number of beta protein subunits=2

Total number of protein sub-units=2+4=6

We have to find the number of different arrangements are there.

When r identical letters and y identical letters and total object are n then arrangements are

[tex]\frac{n!}{r!x!}[/tex]

n=6,r=2,x=4

By using the formula

Then, we get

Number of different arrangements =[tex]\frac{6!}{2!4!}[/tex]

Number of different arrangements=[tex]\frac{6\times 5\times 4!}{2\times 1\times 4!}[/tex]

Number of different arrangements=15

Hence, different arrangements are there= 15

Answer:

(a) Type II error

(b) Type I error

(c) It is analogous to choosing a lower value for a hypothesis test

(d) There will be more tendency of making type II error and less tendency of making type I error

Step-by-step explanation:

(a) The bank made a type II error because they accepted the null hypothesis when it is false

(b) The bank made a type I error because they rejected the null hypothesis when it is true

(c) By lowering the value for the hypothesis test, they give applicants who do not meet the initial cut-off point the benefit of doubt of repaying the loan thus increasing their chances of making more profit

(d) There will be more tendency of making type II error because the bank accepts the null hypothesis though they are not fully convinced the applicants will repay the loan and less tendency of making type I error because the bank rejects the null hypothesis knowing the applicants might not be able to repay the loan

In hypothesis testing, a person defaulting on a loan represents a Type I error, while missing an opportunity to make a loan to someone who would have repaid it represents a Type II error. Lowering the cut-off score is analogous to increasing the value in a hypothesis test, accepting more risk. This increases the likelihood of Type I errors but decreases the likelihood of Type II errors.

In the context of hypothesis testing in banking and the financial capital market, (a) when a person defaults on a loan, the bank made a Type I error: they lent money to an individual who failed to repay it. (b) If the bank does not lend money to someone who would have repaid it, it's a Type II error: they missed an opportunity to profit from interest because they incorrectly predicted the person would not pay back the loan. (c) Lowering the cut-off score from 250 points to 200 is analogous to choosing a higher value for a hypothesis test, which means the bank is willing to accept more risk. (d) Changing the cut-off value impacts the chance of each kind of error. By lowering the score, the bank is more likely to make Type I errors (lending to individuals who won't repay), but less likely to make Type II errors (not lending to individuals who would repay).

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The hypothesis test examines if the company's hiring distribution differs from industry standards. The null hypothesis represents no difference, while the alternative suggests a discrepancy.

The critical value for the test statistic at a 0.05 significance level is ±1.96 for a two-tailed test, and we either reject or fail to reject the null based on the comparison of the calculated Chi-square statistic to the critical value.

To determine if there is a significant difference between the hiring practices of a certain company and the industry standard, we use a hypothesis test for proportions.

A. Null Hypothesis (H₀)

The null hypothesis H0: P_(men) = 0.60 and P_(women) = 0.40, where P represents the proportion of men and women in the company, respectively.

B. Alternative Hypothesis (Ha)

The alternative hypothesis Ha: P_(men) ≠ 0.60 and P_(women) ≠ 0.40.

C. Critical Value of Test Statistic

The critical value for a two-tailed test at alpha = 0.05 is z = ±1.96.

D. Value of the Test Statistic

To calculate the test statistic, we use the formula for a test of proportions:

Calculate the expected counts based on industry proportions: expected men = 107 * 0.60 = 64.2, expected women = 107 * 0.40 = 42.8.

Compute the Chi-square test statistic: Χ2 = ((52-64.2)2/64.2) + ((55-42.8)2/42.8).

The resulting Χ₂ statistic can then be compared against the critical Χ₂ value with 1 degree of freedom at alpha = 0.05, which is 3.841.

E. Reject or Accept the Null Hypothesis

If the calculated Χ₂ is greater than 3.841, we reject the null hypothesis; if not, we fail to reject the null hypothesis. Without the actual calculation of the Χ₂, we cannot definitively conclude the action on the null hypothesis in this context.

Option C

Expression that shows the savings that are being offered on the computer is 0.3p

Solution:

Given that price of a new computer is p dollars

The computer is on sale for 30% offer

To find: Expression that shows the savings that are being offered on the computer

Computer is on sale for 30% offer which means 30 % offer on original price "p"

Original price = "p" dollars

offer price / saved price = 30 % of "p"

[tex]\text{ saved price } = 30 \% \times p\\\\\text{ saved price } = \frac{30}{100} \times p\\\\\text{ saved price } = 0.3p[/tex]

Thus the required expression is 0.3p

Thus option C is correct.

Final answer:

The critical value for constructing a 99% confidence interval is 2.576.

Explanation:

To determine the critical value for constructing the 99% confidence interval, we need to find the Z-value that represents the level of confidence. For a 99% confidence interval, the alpha level (1 - confidence level) is 0.01. Since the data is approximately normally distributed and the sample size is greater than 30, we can use the Z-distribution. Using a Z-table or calculator, we find that the Z-value for a 0.01 alpha level is approximately 2.576.

Answer:

B

Step-by-step explanation:

The retrospective or historic cohort story, is a longitudinal cohort story that considers a particular set of individuals that share the same exposure factor to ascertain its influence in the developments of an occurrence, which are compared with the other set or cohort which were not exposed to the same factors.

Retrospective studies have existed about the same time as prospective studies, hence their names.

Answer:

X = 87.5

Y = 137.5

Step-by-step explanation:

Let's X and Y be the xy-coordinates of the center warehouse.

We know that X is in between the x coordinates or the 2 plants:

50 < X < 150

Similarly Y is in between the y coordinates or the 2 plants:

100 < Y < 200

Using centroid method with the shipping units being weight we can have the following equations

250*50 + 150*150 = X*(250 + 150)

Hence X = (250*50 + 150*150)/(250+150) = 87.5

Similarly 250*100 + 150*200 = Y*(250 + 150)

Hence Y =  (250*100 + 150*200)/(250+150) = 137.5

Answer:

a) [tex]v(t) = 3t^{2} - 16t + 2[/tex]

b) The velocity after 3 seconds is -3m/s.

c) [tex]t = 0.13s[/tex] and [tex]t = 5.2s[/tex].

Step-by-step explanation:

The position is given by the following equation.

[tex]s(t) = t^{3} - 8t^{2} + 2t[/tex]

(a) Find the velocity at time t.

The velocity is the derivative of position. So:

[tex]v(t) = s^{\prime}(t) = 3t^{2} - 16t + 2[/tex].

(b) What is the velocity after 3 seconds?

This is v(3).

[tex]v(t) = 3t^{2} - 16t + 2[/tex]

[tex]v(3) = 3*(3)^{2} - 16*(3) + 2 = -19[/tex]

The velocity after 3 seconds is -3m/s.

(c) When is the particle at rest?

This is when [tex]v(t) = 0[/tex].

So:

[tex]v(t) = 3t^{2} - 16t + 2[/tex]

[tex]3t^{2} - 16t + 2 = 0[/tex]

This is when [tex]t = 0.13s[/tex] and [tex]t = 5.2s[/tex].

Answer:

The volume of the solid is 256 cubic units.

Step-by-step explanation:

Given:

The solid lies between planes [tex]x=0\ and\ x=8[/tex]

The cross section of the solid is a square with diagonal length equal to the distance between the parabolas [tex]y=-2\sqrt{x}\ and\ y=2\sqrt{x}[/tex].

The distance between the parabolas is given as:

[tex]D=2\sqrt x-(-2\sqrt x)\\\\D=2\sqrt x+2\sqrt x\\\\D=4\sqrt x[/tex]

Now, we know that, area of a square with diagonal 'D' is given as:

[tex]A=\frac{D^2}{2}[/tex]

Plug in [tex]D=4\sqrt x[/tex]. This gives,

[tex]A=\frac{(4\sqrt x)^2}{2}\\\\A=\frac{16x}{2}\\\\A=8x[/tex]

Now, volume of the solid is equal to the product of area of cross section and length [tex]dx[/tex]. So, we integrate it over the length from [tex]x=0\ to\ x=8[/tex]. This gives,

[tex]V=\int\limits^8_0 {A} \, dx\\\\V=\int\limits^8_0 {(8x)} \, dx\\\\V=8\int\limits^8_0 {(x)} \, dx\\\\V=8(\frac{x^2}{2})_{0}^{8}\\\\V=4[8^2-0]\\\\V=4\times 64\\\\V=256\ units^3[/tex]

Therefore, the volume of the solid is 256 cubic units.

This question is about volume calculation using calculus. The solid between two planes at x=0 and x=8 has cross-sections which, when described by a function of x A(x), the volume of the object can be computed via integration of A(x) dx from x=0 to x=8.

The subject of this question falls under the field of Calculus, specifically, it's about Volume Calculation. The question describes a solid which is located between two planes at x=0 and x=8, perpendicular to the x-axis. Cross-sections perpendicular to the axis of this solid can be visualized like slices of the solid made along the x-axis.

If the area of these cross-sections can be represented by a function of x, A(x), then the volume of the entirety of the solid, V, can be calculated using the definite integral from x=0 to x=8 of A(x) dx. Essentially, this is summing up the volumes of the infinitesimal discs that make up the solid along the x-axis, from x=0 to x=8.

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Answer:

The expected number of vehicles owned to two decimal places is: 1.85.

Step-by-step explanation:

The table to the question is attached.

[tex]E(X) =[/tex]∑[tex]xp(x)[/tex]

Where:

E(X) = expected number of vehicles owned

∑ = Summation

x = number of vehicle owned

p(x) = probability of the vehicle owned

[tex]E(X) = (0 * 0.1) + (1 * 0.35) + (2 * 0.25) + (3 * 0.2) + (4 * 0.1)\\E(X) = 0 + 0.35 + 0.50 + 0.60 + 0.4\\E(X) = 1.85[/tex]

The expected number of vehicles owned is 1.85.

The expected number of vehicles owned, based on probability of ownership of 0 to 3 vehicles, is calculated by multiplying each possible number of vehicles by their corresponding probabilities and then summing up all the products. The calculated expected number is approximately 1.7 vehicles.

To find the expected number of vehicles owned, we first need to multiply each possible number of vehicles someone could own by the probability of them owning that many vehicles. Then, sum up all of these products.

For instance, if they could own up to 3 cars and the probability for owning 0, 1, 2, or 3 cars is 0.1, 0.3, 0.4, and 0.2 respectively:

For 0 cars: 0 * 0.1 = 0

For 1 car: 1 * 0.3 = 0.3

For 2 cars: 2 * 0.4 = 0.8

For 3 cars: 3 * 0.2 = 0.6    

Adding these together gives the expected number of cars:
0 + 0.3 + 0.8 + 0.6 = 1.7 (rounded to two decimal places).

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Answer:

[tex] P(T<600)=P(Z< \frac{600-576}{144})=P(Z<0.167)=0.566[/tex]

Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}, x>0[/tex]

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

[tex]X \sim Exp(\lambda=\frac{1}{16})[/tex]

Or equivalently:

[tex]X \sim Exp(\mu=16)[/tex]

Solution to the problem

For this case we are interested in the total T, and we can find the mean and deviation for this like this:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}=\frac{T}{n}[/tex]

If we solve for T we got:

[tex] T= n\bar X[/tex]

And the expected value is given by:

[tex] E(T) = n E(\bar X)= n \mu= 16*36=576[/tex]

And we can find the variance like this:

[tex] Var(T) = Var(n\bar X)=n^2 Var(\bar X)= n^2 *\frac{\sigma^2}{n}=n \sigma^2[/tex]

And then the deviation is given by:

[tex]Sd(T)= \sqrt{n} \sigma=\sqrt{16} *36=144[/tex]

And the distribution for the total is:

[tex] T\sim N(n\mu, \sqrt{n}\sigma)[/tex]

And we want to find this probability:

[tex] P(T< 600)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{T- \mu_T}{\sigma_T}[/tex]

And replacing we got this:

[tex] P(T<600)=P(Z< \frac{600-576}{144})=P(Z<0.167)=0.566[/tex]

Using the central limit theorem, the probability that the sum of the lifetimes of 16 light bulbs is less than 600 hours is found to be approximately 0.2514 after calculating the mean, standard deviation, and z-score for the sum.

To estimate the probability that the sum of the lifetimes of 16 light bulbs is less than 600 hours, we can use the central limit theorem. This theorem suggests that the sum (or average) of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the original distribution of the variables. Here, each light bulb's lifetime is an exponential random variable with a mean of 36 hours.

First, we need to determine the mean (μ) and standard deviation (σ) of the sum of the lifetimes. For one light bulb, the mean is 36 hours, and since the standard deviation for an exponential distribution is equal to its mean, it is also 36 hours. For 16 light bulbs, the mean of the sum is 16 * 36 = 576 hours, and the standard deviation of the sum is √16 * 36 = 144 hours due to the square root rule for variances of independent sums.

To find the probability that the sum is less than 600 hours, we convert this to a standard normal distribution problem by calculating the z-score:

Z = (X - μ) / (σ/sqrt(n))
Z = (600 - 576) / (144/sqrt(16))
Z = 24 / 36
Z = 0.67

Now we look up the cumulative probability for a z-score of 0.67 using a standard normal distribution table or a calculator with normal distribution functions. The probability associated with a z-score of 0.67 is approximately 0.7486. Therefore, the probability that the sum of the lifetimes is less than 600 hours is 1 - 0.7486 = 0.2514.

The matching is as follow:

a -> Statistic

b -> Data Sample

d -> Variable

e -> Parameter

f -> Population

a. Statistic: The proportion of the 380 observed people who buy the product

b. Data Sample: The 380 randomly selected people who are observed to see if they will buy the product

d. Variable: Purchase - Yes or No whether a person bought the product

e. Parameter: The proportion of all people in the company's region who buy the product

f. Population: All people in the marketing company's region

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The 380 randomly selected people are the 'Data Sample', the proportion of these who buy is a 'Statistic', all people in the region are the 'Population', the list of 380 Yes/No answers is the 'Variable', proportion of all people in the region who buy the product is 'Parameter', and yes/no answer for each person's purchase is also deemed a 'Variable'.

In this question, we are dealing with terms related to statistic studies. The 380 randomly selected people who are observed to see if they will buy the product represent the Data Sample. The proportion of the 380 observed people who buy the product is considered a Statistic. All people in the marketing company's region is the Population. The list of the 380 Yes or No answers to whether the person bought the product constitutes the Variable. The proportion of all people in the company's region who buy the product is an example of a Parameter. Lastly, the Purchase: Yes or No whether a person bought the product is the Variable.

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Answer:

The variance of the data is 29966.3.

Step-by-step explanation:

The given data set is

175, 349, 234, 512, 638, 549, 500, 611

We need to find the variance to the nearest hundredth decimal place.

Mean of the data

[tex]Mean=\dfrac{\sum x}{n}[/tex]

where, n is number of observation.

[tex]Mean=\dfrac{3568}{8}=446[/tex]

The mean of the data is 446.

[tex]Variance=\dfrac{\sum (x-mean)^2}{n-1}[/tex]

[tex]Variance=\dfrac{(175-446)^2+(349-446)^2+(234-446)^2+(512-446)^2+(638-446)^2+(549-446)^2+(500-446)^2+(611-446)^2}{8-1}[/tex]

[tex]Variance=\dfrac{209764}{7}[/tex]

[tex]Variance=29966.2857[/tex]

[tex]Variance\approx 29966.3[/tex]

Therefore, the variance of the data is 29966.3.

Final answer:

The variance of the given data set is calculated by finding the mean, squaring the differences from the mean, summing these squares, and dividing by the count minus one. It results in a variance of 12790.54 when rounded to the nearest hundredth decimal place.

Explanation:

To calculate the variance of the data set, follow these steps:

First, find the mean (average) of the data set by adding all the numbers together and dividing by the total count.

Next, subtract the mean from each data point and square the result to get the squared differences.

Then, add up all of the squared differences.

Finally, divide the sum of the squared differences by the total number of data points minus one to get the variance (since this is a sample variance).

Data Set: 175, 349, 234, 512, 638, 549, 500, 611

Mean = (175 + 349 + 234 + 512 + 638 + 549 + 500 + 611) / 8 = 3793 / 8 = 474.125

Squared differences = (175 - 474.125)^2 + (349 - 474.125)^2 + (234 - 474.125)^2 + (512 - 474.125)^2 + (638 - 474.125)^2 + (549 - 474.125)^2 + (500 - 474.125)^2 + (611 - 474.125)^2

Sum of squared differences = 89533.78125

Variance = 89533.78125 / (8 - 1) = 12790.54

Therefore, the variance of the data set, to the nearest hundredth decimal place, is 12790.54.

Answer:

The statement b) is individually sufficient to prove than 289 is a factor of n

Step-by-step explanation:

The least common multiple of n and 272 is the smallest number that is a multiple of n and a multiple of 272. Therefore:

272 x X = 4624 ⇒ X = 17 but 272 = 17 · 16 and 289 = 17 · 17

Therefore 17·17 must be a factor of n. That means 289 is a factor of n

Answer:

The procedure emphasizes the idea of the summation of one physical quantity. In this case, X.

Step-by-step explanation:

1. When we add fractions like these we do it simply by rewriting a new one, the summation of the numerators over the same denominator:

[tex]\frac{2}{3}X+\frac{4}{3})X=\frac{6}{3}X= 2X[/tex]

The procedure emphasizes the idea of the summation of one physical quantity, in this case, X.

2) This physical quantity x could be miles, oranges, gallons, etc.

Answer:0.8 kilograms

800 grams

Step-by-step explanation:

The weight of Tyler's baseball bat is 28 ounces. We would convert the weight in ounces to kilogram and grams.

Let x represent the number of kilograms that is equal to 28 ounces. Therefore

1 kilogram = 35 ounces

x kilogram = 28 ounces

Cross multiplying, it becomes

35 × x = 28 × 1

35x = 28

x = 28/35 = 0.8 kilograms

We would convert 0.8 kilograms to grams

Let y represent the number of grams that is equal to 0.8 kilograms. Therefore,

1000 grams = 1 kilogram

y grams = 0.8 kilograms

Cross multiplying,

y × 1 = 0.8 × 1000

y = 800 grams

Answer:

0.2

Step-by-step explanation:

Answer:

a. .8

Step-by-step explanation:

The point estimate of the difference between the means of Company 1 and Company 2 can be calculated as:

point estimate = mu1 - mu2 where

Therefore point estimate = $10.80- $10 =$ .8

Answer:

The number of cellphones to be produced per week is 500.

The cost of each cell phone is $250.

The maximum revenue is $1,25,000

Step-by-step explanation:

We are given the following information in the question:

The weekly​ price-demand equation:

[tex]p(x)=500-0.5x[/tex]

The cost equation:

[tex]C(x) = 25000+140x[/tex]

The revenue equation can be written as:

[tex]R(x) = p(x)\times x\\= (500-0.5x)x\\= 500x - 0.5x^2[/tex]

To find the maximum value of revenue, we first differentiate the revenue function:

[tex]\displaystyle\frac{dR(x)}{dx} = \frac{d}{dx}(500x - 0.5x^2) = 500-x[/tex]

Equating the first derivative to zero,

[tex]\displaystyle\frac{dR(x)}{dx} = 0\\\\500-x = 0\\x = 500[/tex]

Again differentiating the revenue function:

[tex]\displaystyle\frac{dR^2(x)}{dx^2} = \frac{d}{dx}(500 - x) = -1[/tex]

At x = 500,

[tex]\displaystyle\frac{dR^2(x)}{dx^2} < 0[/tex]

Thus, by double derivative test, R(x) has the maximum value at x = 500.

So, the number of cellphones to be produced per week is 500, in order to maximize the revenue.

Price of phone:

[tex]p(500)=500-0.5(500) = 250[/tex]

The cost of each cell phone is $250.

Maximum Revenue =

[tex]R(500) = 500(500) - 0.5(500)^2 = 125000[/tex]

Thus, the maximum revenue is $1,25,000

Final answer:

To find the nth Fibonacci number, dynamic programming stores previously calculated values in an array, which allows for efficient linear time computation by summing the two previous numbers to obtain the nth value.

Explanation:

The Fibonacci sequence is defined such that each number in the sequence is the sum of the two preceding ones, starting from 0 and 1. To calculate the nth Fibonacci number, denoted as Fib(n), we start by setting Fib(0) and Fib(1) equal to 0 and 1, respectively. For n ≥ 2, Fib(n) is defined recursively as Fib(n) = Fib(n - 1) + Fib(n - 2). A naive recursive algorithm could be inefficient due to repeated calculations. Using dynamic programming or memoization improves efficiency by storing intermediate results, thus avoiding unnecessary recalculations.

Computing Fibonacci Numbers Using Dynamic Programming

To compute the nth Fibonacci number using dynamic programming, we create an array or list to save previously computed Fibonacci numbers. The nth value, for instance Fib(8) = 21, is then easily found by summing up the n-1th and n-2th values from the array, which are already computed and stored. This approach leads to a time complexity that is linear, i.e., O(n), instead of exponential.

Answer: a. −0.41

Step-by-step explanation:

The slope for the best-fitting linear equation is given by :-

[tex]b=\dfrac{SS_{xy}}{SS_x}[/tex]

where , [tex]SS_x[/tex] =sum of squared deviations from the mean of X.

[tex]SS_{xy}[/tex] = correlation between y and x in terms of the corrected sum of products.

As per given , we have

[tex]SS_x=10.00[/tex]

[tex]SS_{xy}=-16.32[/tex]

Then, the value of the slope for the best-fitting linear equation will be

[tex]b=\dfrac{-16.32}{40.00}=-0.408\approx -0.41[/tex]

Hence, the value of the slope for the best-fitting linear equation= -0.41

So the correct answer is a. −0.41 .

The value of the slope for the best-fitting linear equation is -0.41

The given parameters are:

[tex]SS_{xy} = -16.32[/tex] --- the correlation between y and x

[tex]SS_{x} = 40.00[/tex] --- the sum of squared deviations from the mean of X.

The slope (b) is calculated using the following formula

[tex]b = \frac{SS_{xy}}{SS_x}[/tex]

Substitute values for SSxy and SSx

[tex]b = \frac{-16.32}{40.00}[/tex]

Divide -16.32 by 40.00

[tex]b = -0.408[/tex]

Approximate

[tex]b = -0.41[/tex]

Hence, the value of the slope for the best-fitting linear equation is -0.41

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Answer:

0.23.

Step-by-step explanation:

We have been given that the weight of people on a college campus are normally distributed with mean 185 pounds and standard deviation 20 pounds.

First of all, we will find the z-score corresponding to sample score 200 using z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=[/tex] Z-score,

[tex]x=[/tex] Sample score,

[tex]\mu=[/tex] Mean,

[tex]\sigma=[/tex] Standard deviation.

[tex]z=\frac{200-185}{20}[/tex]

[tex]z=\frac{15}{20}[/tex]

[tex]z=0.75[/tex]

Now, we need to find [tex]P(z>0.75)[/tex]. Using formula  [tex]P(z>a)=1-P(z<a)[/tex], we will get:

[tex]P(z>0.75)=1-P(z<0.75)[/tex]

Using normal distribution table, we will get:

[tex]P(z>0.75)=1-0.77337 [/tex]

[tex]P(z>0.75)=0.22663 [/tex]

Round to nearest hundredth:

[tex]P(z>0.75)\approx 0.23[/tex]

Therefore, the probability that a person weighs more than 200 pounds is approximately 0.23.

Answer:the probability that a person weighs more than 200 pounds is 0.23

Step-by-step explanation:

Since the weight of people on a college campus are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = weight of people on a college campus

u = mean weight

s = standard deviation

From the information given,

u = 185

s = 20

We want to find the probability that a person weighs more than 200 pounds. It is expressed as

P(x greater than 200) = P(x greater than 200) = 1 - P(x lesser than lesser than or equal to 200).

For x = 200,

z = (200 - 185)/20 = 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.7735

P(x greater than 200) = 1 - 0.7735 = 0.23

Answer:

Step-by-step explanation:

Feel free to ask if anything is unclear

Step-by-step explanation:

Since the decision is made on the test based on the use of alpha equals 0.025, the p-value of the test would have been higher than the level of significance provided that is 0.025 since the test is not important.

p > 0.025

Now if we know that p > 0.025, this would not necessarily mean that p > 0.1 also, therefore we do not know with the given information that he would have made the same decision for 0.1 level of significance, ( we are not sure about his decision in that case ).

Now for the level of significance of 0.005, we would be sure that p > 0.005 as it is greater than 0.025, therefore the test is not significant at this level of significance as well. Therefore he would have made the same decision for 0.005 level of significance.

Answer:

Convenience sampling. See explanation below.

Step-by-step explanation:

For this case they not use random sampling since all the individuals for the population are not included on the sampling frame, some individuals have probability of inclusion 0, because they are just using a charge for the call and some people would not answer the call.

Is not stratified sampling since we don't have strata clearly defined on this case, and other important thing is that in order to apply this method we need homogeneous strata groups and that's not satisfied on this case.

Is not systematic sampling since they not use a random number or a random starting point, and is not mentioned, they just use a call that is charge with 50 cents.

Is not cluster sampling since we don't have clusters clearly defined, and again in order to apply this method we need homogeneous characteristics on the clusters and an equal chance of being a part of the sample, and that's not satisfid again with the call charge used.

So then the only method that can be possible for this case is convenience sampling because they use a non probability sampling with some members of the potential population with probability of inclusion 0.

The sampling technique used in the given scenario is voluntary response sampling, where participants decide whether to take part in the survey. In this technique, participants chose to respond to the television survey by making a call. This method can be biased as the responses could lean towards those who hold strong views on the topic.

The sampling technique used in this scenario is referred as voluntary response sampling or self-selection sampling. In this method, participants themselves decide to participate or not, usually by responding to a call for participants. This often happens when surveys are disseminated widely such as through television or online. Since there was a call to answer "yes" or "no" for the question with a charge, individuals chose to participate by making a call. It is important to note that the main drawback of this technique is that it tends to be biased, as the sample could be skewed in favor of those who felt strongly about the topic.

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Answer:

D. method of least squares

Step-by-step explanation:

The Least Squares Method (LSM) is a mathematical method used to solve various problems, based on minimizing the sum of the squared deviations of some functions from the desired variables. It can be used to “solve”                  over-determined systems of equations (when the number of equations exceeds the number of unknowns), to find a solution in the case of ordinary (not redefined) linear or nonlinear systems of equations, to approximate the point values ​​of a function. OLS is one of the basic regression analysis methods for estimating the unknown parameters of regression models from sample data.

Correlation analysis is a statistical method used to assess the strength of the relationship between two quantitative variables. A high correlation means that two or more variables have a strong relationship with each other, while a weak correlation means that the variables are hardly related. In other words, it is a process of studying the strength of this relationship with available statistics.

Analysis of Variance (or ANOVA) is a collection of statistical models used to analyze group averages and related processes (such as intra- and inter-group variation) in statistical science. When using Variance Analysis, the observed variance of a specified variable is divided into the variance component that can be based on different sources of change. In its simplest form, "Analysis of Variance" is a inferential statistical test to test whether the averages of several groups are equal or not, and this test generalizes the t-test test for two-groups to multiple-groups. If multiple two-sample-t-tests are desired for multivariate analysis, it is clear that this results in increased probability of type I error. Therefore, the variance analysis would be more useful to compare the statistical significance of three or more means (for groups or for variables) with the test.

Regression analysis is an analysis method used to measure the relationship between two or more variables. If analysis is performed using a single variable, it is called univariate regression, and if more than one variable is used, it is called multivariate regression analysis. With the regression analysis, the existence of the relationship between the variables, if there is a relationship between the strength of the information can be obtained. The logic here is that the variable to the left of the equation is affected by the variables to the right. The variables on the right are not affected by other variables. Not being influenced here means that when we put these variables into a linear equation in mathematical sense, it has an effect. Multiple linearity, sequential dependency problems are not meant.

Answer:

Step-by-step explanation:

Hello!

You have two study variables

X₁: Time it takes to get to school by bus.

X₂: Time it takes to get to school by car.

Data:

Sample 1

Bus:(15,10,7,13,14,9,8,12,15,10,13,13,8,10,12,11,14,11,9,12)

n₁= 20

Mean X[bar]₁= 11.30

S₁= 2.39

Sample 2

Car:(5,8,7,6,9,12,11,10,9,6,8,10,13,12,9,11,10,7)

n₂= 18

Mean X[bar]₂= 9.06

S₂= 2.29

A.

To test if there is any difference between the times it takes to get to school using the bus or a car you need to compare the means of each population.

The condition needed to make a test for the difference between means is that both the independent population should have a normal distribution.

The sample sizes are too small to use an approximation with the CLT. You can test if the study variables have a normal distribution using different methods, and hypothesis test, using a QQ-plot or using the Box and Whiskers plot. The graphics are attached.

As you can see both samples show symmetric distribution, the boxes are proportioned, the second quantile (median) and the mean (black square) are similar and in the center of the boxes. The whiskers have the same length and there are no outliers. Both plots show symmetry centered in the mean consistent with a normal distribution. According to the plots you can assume both variables have a normal distribution.

The next step to select the statistic to test the population means is to check whether there is other population information available.

If the population variances are known, you can use the standard normal distribution.

If the population variances are unknown, the distribution to use is a Student's test.

If the unknown population variances are equal, you can use a t-test with a pooled sample variance.

If the unknown population variances are not equal, the t-test to use is the Welch approximation.

Using an F-test for variance homogeneity the p-value is 0.43 so at a 0.01 level, you can conclude that the population variances are equal.

The statistic to use is a pooled t-test.

B.

Degrees of freedom.

For each study variable, you can use a t-test with n-1 degrees of freedom.

For X₁ ⇒ n₁-1 = 20 - 1 = 19

For X₂ ⇒ n₂-1 = 18 = 17

For X₁ + X₂ ⇒ (n₁-1) + (n₂-1)= n₁ + n₂ - 2= 20 + 18 - 2= 36

C.

See above.

D.

The formula for the 99% confidence interval is:

(X[bar]₁ - X[bar]₂) ± [tex]t_{n_1+n_2-2; 1- \alpha /2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} + \frac{1}{n_2} }[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} }[/tex]

[tex]Sa= \sqrt{\frac{19*(2.39)^2+17*(2.29)^2}{36} }[/tex]

Sa= 2.34

[tex]t_{n_1+n_2-2; 1- \alpha /2}[/tex]

[tex]t_{36; 0.995}[/tex] = 2.72

(11.30 - 9.06) ± 2.72 * [tex]2.34\sqrt{\frac{1}{20} + \frac{1}{18} }[/tex]

[0.17;4.31]

With a 99% confidence level you'd expect that the difference between the population means of the time that takes to get to school by bus and car is contained in the interval [0.17;4.31].

E.

Couldn't find the original lesson to see what calculator is used.

F.

Same, no calculator available.

I hope it helps!

Answer:

this is nnot the answer i was looking for

Step-by-step explanation:

Answer:

The expected value is 1.8

Step-by-step explanation:

Consider the provided information.

Suppose there’s a 15%  chance of having 0 announcements, a 30% chance of having 1 announcement, a 25% chance of  having 2 announcements, a 20% chance of having 3 announcements, and a 10% chance of having 4  announcements.

[tex]\text{Expected Value}=a \cdot P(a) + b \cdot P(b) + c \cdot P(c) + \cdot\cdot[/tex]

Where a is the announcements and P(a) is the probability.

[tex]\text{Expected Value}=0\cdot 15\% + 1 \cdot 30\% + 2 \cdot 25\% + 3\cdot20\%+4\cdot10[/tex]

[tex]\text{Expected Value}=1 \cdot 0.30+2 \cdot 0.25 +3 \cdot 0.2 + 4\cdot 0.10[/tex]

[tex]\text{Expected Value}=1.8[/tex]

Hence, the expected value is 1.8

Answer:

[tex]\cos (\frac{1}{t^3}-6)} + c[/tex]

Step-by-step explanation:

Given  function:

[tex]\int {\frac{3}{t^4}\sin (\frac{1}{t^3}-6)} \, dt[/tex]

Now,

let [tex]\frac{1}{t^3}-6[/tex] be 'x'

Therefore,

[tex]d(\frac{1}{t^3}-6)[/tex] = dx

or

[tex]\frac{-3}{t^4}dt[/tex] = dx

on substituting the above values in the equation, we get

⇒ ∫ - sin (x) . dx

or

⇒ cos (x) + c                      [ ∵ ∫sin (x) . dx = - cos (x)]

Here,

c is the integral constant

on substituting the value of 'x' in the equation, we get

[tex]\cos (\frac{1}{t^3}-6)} + c[/tex]