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

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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
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