Question

Translate each of the following research questions into appropriate H0 and Ha.

(a) Census Bureau data show that the mean household income in the area served by a shopping mall is $62,500 per year. A market research firm questions shoppers at the mall to find out whether the mean household income of mall shoppers is higher than that of the general population.

(b) Last year, your company's service technicians took an average of 2.6 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year's data show a different average response time?

Answer 1

a)

`H_(0): \mu = 62500\text{ dollars per year}\\H_A: \mu > 62500\text{ dollars per year}`

b)

`H_(0): \mu = 2.6\text{ hours}\\H_A: \mu \\eq 2.6\text{ hours}`

Explanation:

We have to build appropriate null and alternate hypothesis for the given scenarios.

a) Population mean, μ = $62,500 per year

The market research wants to find whether the mean household income of mall shoppers is higher than that of the general population.

`H_(0): \mu = 62500\text{ dollars per year}\\H_A: \mu > 62500\text{ dollars per year}`

We would use one-tail(right) test to perform this hypothesis.

b) Population mean, μ = 2.6 hours

The company want to know the average time to respond to trouble calls is different or not.

`H_(0): \mu = 2.6\text{ hours}\\H_A: \mu \\eq 2.6\text{ hours}`

We would use two-tail test to perform this hypothesis.