Exhibit 10 . 4 . A 7000-seat theater is interested in determining whether there

Question

Exhibit 10.4.

A 7000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5500, while the mean attendance on Wednesday evening is calculated as 5850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445.

Refer to Exhibit 10.4. What is the appropriate decision given a 5% level of significance?

A) Conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.

B) Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

C) Do not conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.

D) Do not conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

A) Conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.

B) Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

C) Do not conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.

D) Do not conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

Explanation / Answer

The statistical software output for this problem is:

Two sample Z summary hypothesis test:
1 : Mean of population 1 (Std. dev. = 550)
2 : Mean of population 2 (Std. dev. = 445)
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0

Hypothesis test results:

Hence,

Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

Option B is correct.

Difference n1 n2 Sample mean Std. err. Z-stat P-value 1 - 2 25 25 -350 141.49558 -2.4735754 0.0134

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