Question

A manufacturer claims that the mean lifetime of its lithium batteries is 1400 hours. A homeowner selects 30 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 80 hours. Test the manufacturer's claim using a two-tailed test. Use α = 0.05. Round to 3 decimal places.

1.) State the Null and Alternative Hypotheses (mathematically, not in words).

2.) Specify the critical t values for the rejection region (that is, find the critical region) using the table below or your calculator, draw the t- distribution, and shade the critical/rejection region(s). 3.) Find the test statistic by hand using the formula. -over-

4.) Does the test statistic fall in the rejection region? YES or NO

5.) State the conclusion to your hypothesis test. Circle: Reject the null hypothesis or Do not reject the null hypothesis.

6.) So, is there enough evidence to reject the manufacturer claim that the mean lifetime of its lithium batteries is 1400 hours (Null Hypothesis)? YES or NO

7.) Find the p-value using your calculator (list the function and inputs for partial credit). Determine your conclusion (again-it should be the same as above in e and f) and state why (ie., because the p-value is less than.... or not less than...). p-value: Conclusion: Why:

Answer 1

Given = 1400 hours

Sample statistics

mean = 1380 hours

std dev s = 80 hours

sample size n = 30

1.) Hypothesis

H0:

H1: two tail test

2.) alpha = 0.05

degrees of freedom df = n-1 = 30-1 =29

critcal value = talpha/2,df = t0.025,29 = +/- 2.045

blue region is rejection region.

rejection criteria : It |test statistic | > critical value then reject H0 otherwise fail to reject.

3) test statistic t = = = -1.369

4) No, The test statistic does not fall in rejection region

5) Do not reject the null hypothesis.

6) No, there is no enough evidence to reject the manufacturer claim that the mean lifetime of its lithium batteries is 1400 hours (Null Hypothesis)

7) p-value = 0.1815 , No, there is no enough evidence to reject the manufacturer claim that the mean lifetime of its lithium batteries is 1400 hours (Null Hypothesis) ie., because the p-value is not less than alpha (0.05).