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. A random sample of 25 weeks is collected for Tuesday a different sample of 25 weeks is collected for 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. Let μ₁ be the population mean of Tuesday, μ₂ be the population mean of Wednesday, and μ_D be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening? A) H₀: µ_D ≥ 0, H_A: µ_D

Question

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. A random sample of 25 weeks is collected for Tuesday a different sample of 25 weeks is collected for 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. Let μ₁ be the population mean of Tuesday, μ₂ be the population mean of Wednesday, and μ_D be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening? A) H₀: µ_D ≥ 0, H_A: µ_D<0 B) H₀: µ_D = 0, H_A: µ_D≠0 C) H₀: µ₁ - µ₂ = 0, H_A: µ₁ - µ₂ ≠ 0 D) H₀: µ₁ - µ₂ ≥ 0, H_A: µ₁ - µ₂ < 0

Quizplus · Accepted Answer

We are interested in comparing the mean attendance on Tuesday evening to the mean attendance on Wednesday evening. This is a comparison of two population means. Option A) is incorrect because it only considers the null hypothesis without an alternative hypothesis. We need to consider both hypotheses for a two-tailed test. Option B) is incorrect because it assumes that the difference in means is not equal to zero which is not a valid assumption for a hypothesis test. We need to test whether the difference in means is equal to or not equal to zero, not assume that it is not equal to zero. Option D) is incorrect because it assumes a one-tailed test when we need to consider a two-tailed test. Option C) presents the appropriate null and alternative hypothesis for a two-tailed test. The null hypothesis is that there is no difference between the mean attendance on Tuesday and Wednesday evening (µ₁ - µ₂ = 0). The alternative hypothesis is that there is a difference between the mean attendance on Tuesday and Wednesday evening (µ₁ - µ₂ ≠ 0). This hypothesis test can be conducted using a two-sample t-test for independent samples.

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