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.What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean μ₁ and Wednesday attendance as population 2 mean μ₂,or μ_D as the mean difference in matched-pairs sampling. 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.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.What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean μ₁ and Wednesday attendance as population 2 mean μ₂,or μ_D as the mean difference in matched-pairs sampling. 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

The appropriate hypotheses in this scenario are H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0. This is a two-sample t-test for the difference in means between two independent populations, with equal variances not assumed. The null hypothesis states that there is no difference in attendance between shows on Tuesday evening and Wednesday evening, while the alternative hypothesis states that there is a difference. Choice A is incorrect because it suggests a one-sided alternative hypothesis without specifying the direction of the difference. Choice B is incorrect because it suggests testing for a difference in means without specifying the direction of the difference. Choice D is incorrect because it suggests a one-sided alternative hypothesis with the wrong direction specified.

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