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 94.6 49.2 77.4 43.2 After visit 63.5 101.4 57.8 81.2 41.9 Do the data indicate that the average net sales improved? Use ? = 0.05. (Let d = before − after.) What are we testing in this problem? single proportion or difference of proportions or single mean Or paired difference or difference of means What is the level of significance? State the null and alternate hypotheses. H0: ?d = 0; H1: ?d ≠ 0 H0: ?d ≥ 0; H1: ?d < 0 H0: ?d > 0; H1: ?d ≤ 0 H0: ?d ≠ 0; H1: ?d = 0 What sampling distribution will you use? What assumptions are you making? a.The standard normal. We assume that d has an approximately uniform distribution. b.The Student's t. We assume that d has an approximately uniform distribution. C.The Student's t. We assume that d has an approximately normal distribution. d.The standard normal. 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 > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-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 ?? a.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. c.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. d.At the ? = 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. A.There is sufficient evidence at the 0.05 to conclude that the average net sales have improved. b.There is insufficient evidence at the 0.05 to conclude that the average net sales have improved.

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 94.6 49.2 77.4 43.2 After visit 63.5 101.4 57.8 81.2 41.9 Do the data indicate that the average net sales improved? Use ? = 0.05. (Let d = before − after.) What are we testing in this problem? single proportion or difference of proportions or single mean Or paired difference or difference of means What is the level of significance? State the null and alternate hypotheses. H0: ?d = 0; H1: ?d ≠ 0 H0: ?d ≥ 0; H1: ?d < 0 H0: ?d > 0; H1: ?d ≤ 0 H0: ?d ≠ 0; H1: ?d = 0 What sampling distribution will you use? What assumptions are you making? a.The standard normal. We assume that d has an approximately uniform distribution. b.The Student's t. We assume that d has an approximately uniform distribution. C.The Student's t. We assume that d has an approximately normal distribution. d.The standard normal. 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 > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-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 ?? a.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. c.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. d.At the ? = 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. A.There is sufficient evidence at the 0.05 to conclude that the average net sales have improved. b.There is insufficient evidence at the 0.05 to conclude that the average net sales have improved.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Related questions

Question

100%

Store	1	2	3	4	5
Before visit	57.3	94.6	49.2	77.4	43.2
After visit	63.5	101.4	57.8	81.2	41.9

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

What are we testing in this problem?

single proportion or difference of proportions or single mean Or paired difference or difference of means

What is the level of significance?

State the null and alternate hypotheses.

H₀: ?_d = 0; H₁: ?_d ≠ 0

H₀: ?_d ≥ 0; H₁: ?_d < 0

H₀: ?_d > 0; H₁: ?_d ≤ 0

H₀: ?_d ≠ 0; H₁: ?_d = 0

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

a.The standard normal. We assume that d has an approximately uniform distribution.

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

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

d.The standard normal. 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 > 0.250

0.125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-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 ??

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

b.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

c.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

d.At the ? = 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.

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

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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