Question

A marketing consultant was hired to visit a random sample of five sporting goods stores across...

A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):

Store 1 2 3 4 5
Before visit 57.3 94.4 49.2 77.4 43.2
After visit 63.3 101.6 57.8 81.2 41.9

Do the data indicate that the average net sales improved? Use α = 0.05. (Let d = before − after.)

What are we testing in this problem?

single proportionpaired difference    difference of proportionsdifference of meanssingle mean

What is the level of significance?


State the null and alternate hypotheses.

H0: μd = 0; H1: μd ≠ 0H0: μd ≠ 0; H1: μd = 0    H0: μd > 0; H1: μd ≤ 0H0: μd ≥ 0; H1: μd < 0


What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that d has an approximately normal distribution.The Student's t. We assume that d has an approximately uniform distribution.    The standard normal. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately normal distribution.


What is the value of the sample test statistic? (Round your answer to three decimal places.)


Estimate the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005


Sketch the sampling distribution and show the area corresponding to the P-value.


Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.


Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that the average net sales have improved.There is insufficient evidence at the 0.05 to conclude that the average net sales have improved.

Homework Answers

Answer #1

paired difference  

level of significance =0.05

μd ≥ 0; H1: μd < 0

.The Student's t. We assume that d has an approximately normal distribution.


sample test statistic = -2.810

0.005 < P-value < 0.025

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

There is sufficient evidence at the 0.05 to conclude that the average net sales have improved.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A marketing consultant was hired to visit a random sample of five sporting goods stores across...
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars): Store 1 2 3 4 5 Before...
A marketing consultant was hired to visit a random sample of five sporting goods stores across...
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars): Store 1 2 3 4 5 Before...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent...
Six sets of identical twins were randomly selected from a population of identical twins. One child...
Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from each pair was part of the control group that did not participate in the program to promote creative thinking. At the end of the program, a creative problem-solving test was given, with the results shown in the...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is  smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. The artifact frequency for an excavation of a kiva in Bandelier National Monument gave the following information. Stratum Flaked Stone Tools Nonflaked Stone Tools 1 9 2...
A marketing consultant was hired to visit a random sample of five sporting goods stores across...
A marketing consultant was hired to visit a random sample of five sporting goods stores across Canada. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers a better way to advertise and display their goods. The net sales for 1 month before, and 1 month after the consultant’s visit were recorded as follows for each store (in thousands of dollars): Store 1 2 3 4 5 Before visit 57.1 94.6 49.2 77.4...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 14 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 13.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT