Find the critical value(s) and rejection region(s) for a right-tailed chi-square

Question

Find the critical value(s) and rejection region(s) for a right-tailed chi-square test with a sample size n=15 and level of significance a = 0.05.

Round three decimal places.

A light bulb manufacturer guarantees that the mean of a certain type of light bulb is at least 761 hours. A random sample of 28 light bulbs has a mean of 736 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At significance level a =0.05, do you have enough evidence to reject the manufacturer

Explanation / Answer

1) critical value= 23.685

2)

hypothesis : Ho: mu>=761 (claim)

and alternative hypothesis Ha:mu<761

the critical value     z0.05 =-1.645

rejection region z<- 1.645

The standardized test statistic Z = -2.169.

Decision: reject the null hypothesis

There is sufficient evidence to reject the claim that the mean bulb life is at least 761 hours

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