Question

8. Last year, the mean running time for a certain type of flashlight battery was 8 hours. This year, the manufacturer has introduced a change in the production method which he hopes will increase the mean running time. A random sample of 36 of the new light bulbs was obtained and the mean running time was found to be 8.3 hours with s=1 hours. Do the data provide sufficient evidence to conclude that the mean running time, u, of the new light bulbs is larger than last year's mean of 8 hours? Perform the appropriate hypothesis test using a significance level of 5%. (10 points)

Answer 1

Given that, = 8.3, s=1, n = 36 Null and the alternative hypothesis: H:58 H:\> 8 Significance level, a =0.05 Test statistic: X - ! t= 1 8.3-8 1 136 = 1.80

Degree of freedom: n-1= 36-1 = 35 P-value: Use the excel formula, p = [=TDIST(1.80,35,1)] ((=TDIST(x,df,tails)) = 0.0402 Decision rule: Reject H, if p sa otherwise do not reject H. Since the p-value less than the level of significance, so we reject the null hypothesis at specified significance level. Conclusion: Hence there is sufficient evidence to conclude that the mean running time of the new light bulbs is larger than last years mean of 8 hours