Question

The accompanying table contains a food critic's ratings for food, décor, service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in suburban areas outside the city. You want to study differences in the cost of a meal between restaurants in the city and suburban areas and also want to be able to predict the cost of a meal. Completely analyze the data.

Test for the difference between the mean cost of a city meal and the mean cost of a suburban meal, using α = 0.05.

Choose an appropriate set of hypotheses, where mu 1μ1 is the mean cost of a meal in the city and mu 2μ2 is the mean cost of a meal in the suburbs.

A. H0 : H0: μ1 ≠ μ2 H1 : μ1 = μ2

B. H0 : μ1 = μ2 H1 : μ1 ≠ μ2

C. H0: μ1 > μ2 H1: μ1 = μ2

D. H0: μ1 = μ2 H1 : μ1< μ2

Answer 1

Option B)

`H_(0): \mu_1 = \mu_2\\H_A: \mu_1 \\eq \mu_2`

Explanation:

We are given the following information in the question:

We want to study differences in the cost of a meal between restaurants in the city and suburban areas.

We have to perform a hypothesis test for the difference between the mean cost of a city meal and the mean cost of a suburban meal, using α = 0.05.

First, we design the null and the alternate hypothesis

`H_(0): \mu_1 = \mu_2\\H_A: \mu_1 \\eq \mu_2`

The null hypothesis states that there is no significant difference mean cost of a city meal and the mean cost of a suburban meal that is they are the same.

The alternative hypothesis states that there is a significant difference mean cost of a city meal and the mean cost of a suburban meal that is they are not the same.