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Please explain well! No shortcuts! 8. A manufacturer claims that his television will have an average...

Please explain well! No shortcuts!

8. A manufacturer claims that his television will have an average lifetime of at least five years. 81 televisions are selected at random, and their average lifetime was found to be 62 months, with a standard deviation of 7 months. Is the manufacturer correct? Use the p-value method with α = .05. Hint: work in months, not years.

State your hypotheses:

Calculate the test statistic:

Find the p-value:

State your decision:

Write your conclusion:

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :   = 60

Ha : < 60

Test statistic = z

= ( - ) / / n

= (62 - 60) / 7 / 81

= 2.57

P(z < 2.57) = 0.9949

P-value = 0.9949

= 0.05

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence to conclude that the manufacturer is not correct .

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