8 Before installing a high-tech laser exhibit near the exit area, a museum of Am

Question

8 Before installing a high-tech laser exhibit near the exit area, a museum of American technology found the average contribution by patrons was $2.75 per person. For a sample of 30 patrons following installation of the new exhibit, the contributions are as listed in data file XR10108. Based on the sample data, and using the 0.025 level of significance, can we conclude that the new exhibit has increased the average contribution of exhibit patrons? Identify and interpret the p-value for the test.

4.00
2.80
2.50
3.75
2.80
3.90
3.40
3.60
1.80
2.50
1.70
3.00
3.75
4.20
4.30
2.40
3.60
1.90
3.10
4.50
5.00
4.30
3.10
2.90
4.25
2.60
4.20
3.75
2.50
2.90

A company that makes an athletic shoe designed for basketball has stated in its advertisements that the shoe increases the jumping ability of players who wear it. The general manager of a professional team has conducted a test in which each player’s vertical leap is measured with the current shoe versus the new model, with the data as listed in file XR11099. At the 0.05 level of significance, evaluate the claim that has been made by the shoe company. Identify and interpret the p-value for the test.

1 1 2 3 3 1 3 1 1 3 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 3 3 1 3 3 1 1 3 3 3 1 3 1 1 3 1 1 3 3 3 1 1 3 2 3 1 2 1 1 3 3 3 1 1 1 1 2 1 3 1 1 1 3 3 3 3 3 1 3 3 2 3 1 1 3 3 1 1 1 1 3 1 3 1 3 3 1 3 1 3 1 3 2 1 3 3 3 3 1 1 1 3 3 3 3 3 3 3 1 3 3 2 1 1 3 3 1 3 3 2 3 3 1 1 3 2 3 1 3 1 3 1 1 3 1 3 3 1 3 1 3 2 3 1 3 3 2 1 1 3 1 1 1 1 3 3 1 1 3 1 3 2 2 1 3 1 1 3 1 3 3 1 3 1 3 1 3 3 1 1 1 1 2 3 3 3 1 3 3 3 3

Explanation / Answer

Ho : mu = 2.75

Ha : mu > 2.75

Right tailed test

n = 30 , z-test can be used ,

alpha = 0.025

z critical = 2.01

xbar = 3.3

sd = 0.86063

test statistic = (3.3-2.75)/(0.86063/sqrt(25)) = 3.1953

p-value = 0.0007

since Test-statistic is gretar than critical value ,we reject the null hypothesis , and conclude that

the new exhibit has increased the average contribution of exhibit patrons

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