A 7,000-Seat Theater Is Interested in Determining Whether There Is

question 57

Multiple Choice

A 7,000-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 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. 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. Which of the following is the appropriate decision given a 5% level of significance?

• A) Conclude that the mean attendance differs because the p-value = 0.0067 < 0.05.
• B) Conclude that the mean attendance differs because the p-value = 0.0134 < 0.05.
• C) Do not conclude that the mean attendance differs because the p-value = 0.0067 < 0.05.
• D) Do not conclude that the mean attendance differs because the p-value = 0.0134 < 0.05.

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Definitions:

Percentile

A measure that indicates the value below which a given percentage of observations in a group falls.

Frequency Distribution

A table or chart that gives each piece of data in the set and the frequency, or the number of times that it appears in the data set.

Standard Deviation

A statistic that measures the dispersion or variation of a set of values, indicating how much the values differ from the mean of the set.

Z-score

A statistical measure that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.