Question

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 38 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that μ is less than 38 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 34 minutes and the standard deviation of the times to be 12 minutes.

Based on this information, answer the questions below.

What are the null hypothesis (

H0

) and the alternative hypothesis (

H1

) that should be used for the test?

H0

:

μ

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?341238

H1

:

μ

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?341238

In the context of this test, what is a Type I error?

A Type I error is ?rejectingfailing to reject the hypothesis that

μ

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?341238 when, in fact,

μ

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?341238.

Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be making? ?Type IType II

Answer 1

Solution:

1.The given claim is to test , whether mean μ is less than 38 minutes .

So here Ho: μ = 38

VS Ha : μ < 38

2.In the context of this test, what is a Type I error?

Definition of Type I error: Reject Ho when it is true.

So here , Type I error is we reject Ho: μ = 38 , when in fact μ = 38 is true.

3.Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be making?

As per the definition above , here it is given that consultant reject Ho, so this is type-I error.