Question

A manufacturer of calculator batteries claims that the average lifespan of her batteries is more than 1300 hours. a. Set up the null and alternative hypothesis needed to substantiate this claim, as if you had reason to believe that this claim is not being met. b. A sample of 16 batteries is tested and it is found that the sample mean is 1280 hours and σ = 40 hours. Do a test of your null hypothesis at the 1% significance level.

Answer 1

Given that, i = 1280, 0 = 40, n = 16 Null and the alternative hypothesis: H:u=1300 Hu>1300 Significance level, a = 0.01 Test statistic: X - vn 1280-1300 40 16 = -2.00 P-value: p=P(Z >=) =1-P(Z S-2.00 =1-0(-2.00) =1-0.0228 =0.9772 (Standard normal tables)

Decision rule: Reject H, if psa otherwise do not reject H. Since the p-value greater than the level of significance, so we fail to reject the null hypothesis at specified significance level. Conclusion: There is not sufficient evidence to support the claim that the average lifespan of her batteries is more than 1300 hours