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A company manufacturing light bulbs is testing a new model

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A company manufacturing light bulbs is testing a new model. The company is going to test the hypothesis that the mean life time is 1000 hours vs. the alternative hypothesis that it is less than 1000 hours at the significance level a = 0.02. Assume that the population distribution for life time is approximately normal.

A sample of 16 light bulbs are found to have sample mean X= 987.5 hours and sample variance S2 = 400.0

a) State the critical region and determine whether the null hypothesis Ho is rejected.

b) If the company wants to decrease the probability of making a type 1 error without increasing the sample size, should the critical value be increased or decreased? Justify your answer.

c) Find a 90% confidence interval for the population variance 02

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