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 57.5 94.6 49.2 77.4 43.2 After visit 63.7 101.6 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? paired differencesingle proportion single meandifference of meansdifference of proportions (a) What is the level of significance? State the null and alternate hypotheses. H0: ?d = 0; H1: ?d < 0H0: ?d = 0; H1: ?d ≠ 0 H0: ?d > 0; H1: ?d = 0H0: ?d = 0; H1: ?d > 0 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.The standard normal. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately uniform distribution.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.) (c) Find (or 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	57.5	94.6	49.2	77.4	43.2
After visit	63.7	101.6	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?

paired differencesingle proportion single meandifference of meansdifference of proportions

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?_d = 0; H₁: ?_d < 0H₀: ?_d = 0; H₁: ?_d ≠ 0 H₀: ?_d > 0; H₁: ?_d = 0H₀: ?_d = 0; H₁: ?_d > 0

(b) What sampling distribution will you use? What assumptions are you making?

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

(c) Find (or 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

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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