Question

Question 1 (20 points) 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. 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 and Wednesday attendance as population 2 or μD as the mean difference in matched-pairs sampling/dependen

Answer 1

Answer:

The hypothesis is:

H₀: μ₁ = μ₂.

Hₐ: μ₁ ≠ μ₂.

Step-by-step explanation:

The 7000-seat theater wants to determine whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.

The population on Tuesday evening is denoted by, 1.

The population on Wednesday evening is denoted by, 2.

The information provided is:

$n_{1}=n_{2}=25\\\bar x_{1}=5500\\\bar x_{2}=5850\\\sigma_{1}=550\\\sigma_{2}=445$

As the population standard deviations for the both the populations are known, we will not use t-test for two independent samples or matched pair design/dependent t-test.

We will use the z-test for difference between two means to perform the test.

The hypothesis for the test can be defined as:

H₀: The mean attendance on Tuesday and Wednesday evening are same, i.e. μ₁ = μ₂.

Hₐ: The mean attendance on Tuesday and Wednesday evening are different, i.e. μ₁ ≠ μ₂.