An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. A researcher believes that he can show that the average lifetime of the bulbs is greater than 800 hours, and from a random sample of 25 bulbs finds that the sample average lifetime is 820 hours. What should the researcher conclude about the average lifetime of the bulbs? Be sure to state the null and alternative hypotheses. Use a significance level of 5%.
Given | |
X bar | 820 |
μ | 800 |
σ | 40 |
n | 25 |
Hypothesis:
H0: μ = 800
Ha: μ > 800
Critical value:
Z c = 1.645 (right tailed)(Use Z table)
If Z stat > Z critical, Reject H0
Test:
Z = (X bar-μ )/(σ/SQRT(n)) = (820-800)/(40/SQRT(25)) = 2.5
Decision:
Z stat > Z critical, Reject H0
P value = 0.0062
P value < 0.05, Reject H0
Conclusion:
There is enough evidence to conclude that the average lifetime of the bulbs is greater than 800 hours at 5% significance level
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