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  35  minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that  μ  is less than  35  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  31  minutes and the standard deviation of the times to be  15  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 ?313515 H1 :  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515 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 ?313515 when, in fact,  μ  is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515. Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? ?Type IType II

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 
35
 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that 
μ
 is less than 
35
 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 

31
 minutes and the standard deviation of the times to be 
15
 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 ?313515
H1
μ
 is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515

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 ?313515 when, in fact, 
μ
 is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515.

Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? ?Type IType II
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