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Confidence Interval & Chi-square Test

A random sample of light bulbs had a mean life of xbar = 587 hours. the standard deviation of the lifetime of all such light bulbs is of sigma = 36 hours

#1 construct a 90% confidence interval estimate of the mean life, m, of all light bulbs of this type.

It was expected that the mean lifetime of the bulbs was 600 hours. Do the results contradict expectations? explain your answer.

#2

A worker in an insurance company processes claims. The distribution of the number of claims processed each day in a week of this worker's life as follows.

Day #of claims
Monday 28
Tuesday 45
Wednesday 40
Thursday 23
Friday 29

The worker's boss thinks the worker's claims processing is sporadic and is not evenly distributed throughout the week. at the a=0.05 level, is there sufficient evidence to conclude that the worker's claims processing is sporadic?

Show all work include the hypothesis, the computation of the test statistic, state the critical value, and state the conclusion of the test.

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Confidence Interval & Chi-square Test

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