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

Publisher:Carter

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,

, spent by customers at the supermarkets has been reported to be

minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that

is less than

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

minutes and the standard deviation of the times to be

minutes.

Based on this information, answer the questions below.

What are the null hypothesis (

) and the alternative hypothesis (

) that should be used for the test?

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?313515

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

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

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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