Question

A lightbulb manufacturer has developed a new lightbulb that it claims has an average life of more than 1,000 hours. A random sample of 50 lightbulbs was taken and had a mean of 1,065 hours and standard deviation of 125 hours. Perform a hypothesis test with a level of significance of 0.01.

Perform steps 2 and 3 of the hypothesis test.

Perform step 4 of the hypothesis test using the information from the last question.

Perform step 5 of the hypothesis test. Use your results from the previous lightbulb related questions.

Interpret your decision in the context of the original statement. (Note: Look back at our examples for the general format.)

Answer 1

the given data are :-

sample mean () = 1065

sample sd (s) = 125

sample size (n )= 50

a).hypothesis:-

the manufacturer's claim is the alternative hypothesis.

b).test statistic be:-

c).df = (n-1) = (50-1) = 49

p value :-

[ in any blank cell of excel type =T.DIST.RT(3.677,49) press enter]

d).decision:-

p value = 0.0003 <0.01 (alpha)

so, we reject the null hypothesis.

e).conclusion:-

there is sufficient evidence to support the manufacturer's claim that the average life of the new lightbulb is more than 1,000 hours at 0.01 level of significance.

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