Question

A manufacturer of flashlight batteries took a sample of 15 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed. At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 500 hours?

Data:

426

317

545

264

1049

631

512

366

592

562

298

421

678

345

987

Possible Answers:

• A. No, because the p-value for this test is equal to .2978
• B. Yes, because the p-value for this test is equal to .1164
• C. Yes, because the p-value for this test is equal to .2978
• D. No, because the p-value for this test is equal to .1164

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 500
Alternative Hypothesis, Ha: μ > 500

Rejection Region
This is right tailed test, for α = 0.05 and df = 14
Critical value of t is 1.761.
Hence reject H0 if t > 1.761

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (532.8667 - 500)/(234.4257/sqrt(15))
t = 0.543

P-value Approach
P-value = 0.2978
As P-value >= 0.05, fail to reject null hypothesis.

A. No, because the p-value for this test is equal to .2978