Question

Two supermarket owners each claim that more customers enter their store than the other’s store. Survey was taken and it was found that in 60 days an average of 810 people per day entered the first store with a standard deviation of 40 people. A corresponding survey found that in 80 days an average of 800 people per day entered the second store with a standard deviation of 30 people.

State the hypothesis if this is a two-tailed test.(3pts)

Conduct the two-tailed test with α = .05.(5pts)

Test the hypothesis that µ1 - µ2 = 5 against a two-tailed alternative.(5pts)

Explain under what condition

A Type I error would be committed(3pts)

Answer 1

The provided sample means are shown below :

and the sample size are n1 = 60 and n2 = 80.

(a) Null and alternative Hypotheses

The following null and alternative hypotheses need to be tested

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standrad deviations will be used.

Rejection region

Based on the information provided, the significance level is = 0.05, and the degrees of freedom are df = 105.287. In fact, the degrees of freedon are computed as follows, assuming that the population variances are unequal.