Question

BIG Corporation advertises that its light bulbs have a mean lifetime, u , of 3000 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 2860 hours and that the sample standard deviation of the lifetimes is hours. Based on this information, answer the questions below. What are the null hypothesis (H0) u is less than, less than or equal to, greater than, greater than or equal to , not equal to, equal to 2860. 3000. 700? and the alternative hypothesis (H1) is ( same options above) 2860, 3000, 700? that should be used for the test? : is : is In the context of this test, what is a Type II error? A Type II error is rejecting, failing to reject the hypothesis that is when, in fact, is . Suppose that we decide to reject the null hypothesis. What sort of error might we be making? typeI or type II?

Answer 1

we have given :

u = population mean = 3000

sample mean = 2860 and that the sample standard deviation of the lifetimes is hours

To test :

Null hypothesis (Ho) : u is equal to 3000 ( null hypothesis is always equal to population parameter that is no difference)

and the alternative hypothesis (H 1): is u not equal to 3000 ( Alternative hypothesis is may be not equal to , greater than , less than of the population parameter)

## Note : in hypothesis testing our null and alternative hypothesis is always for the population parameter not sample parameter

yes we should use for test :

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

Answer : Type 2 error is we accept Ho when it is false . that is failing to reject the hypothesis that is when, in fact is.

## Q ) Suppose that we decide to reject the null hypothesis. What sort of error might we be making?

Answer : type I error is we reject Ho when it is true. for reject the null hypothesis we should use Type 1 error