BIG Corporation advertises that its light bulbs have a mean lifetime, μ , of at least 2900 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2760 hours and that the sample standard deviation of the lifetimes is 600 hours. 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 ?27602900600 H1 : μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600 In the context of this test, what is a Type II error? A Type II error is ?rejectingfailing to reject the hypothesis that μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600 when, in fact, μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600. Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? ?Type IType II

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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BIG Corporation advertises that its light bulbs have a mean lifetime,

, of at least

2900

hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is

2760

hours and that the sample standard deviation of the lifetimes is

600

hours.

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 ?27602900600

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600

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

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

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600 when, in fact,

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?27602900600.

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

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