Question

Quiz 3 mean 25.3 samble nsloo 22:3 5 8 .3 Section 212 Q no. 2 (5 points) In a recent year, the Federal Communications Commission reported that the mean wait for repairs for AT&T customers was 25.3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process, used for a sample of 100 repairs, resulted in a sample mean of 22.3 hours and a standard deviation of 8.3 hours. a) Is there evidence that the population mean amount is less than 25.3 hours? (Use a 0.05 level of significance.) b) Determine the p-value and interpret its meaning. He=NZ 25,5 - HIFU < 25. 3 reject 22.3.-25.3

Answer 1

Given that Sample mean X= 22.3 Hours Sample Standard deviation 5 = 8.3 hours Samble size n = 100 Population mean u= 25.3 hours Signibicance level di 0.05 (57) Null Hypothesis (Ho) ; u > 25.3 Alternative Hypothesis (H): u < 25.3 This Gorrsponds to a lett-tailed test for which a t-test for one mean, with unknown Population standard deviation will be used. Rejection Region Based on the information provided the Significance level is 2 = 0.05 and the degrees of freedom dif-n-1=qq. Scanned with CamScanner

From t- table values, the critical value for a lebt -tailed test is te : -1.667 The rejection region for this lett-tailed test is to Raft:< -1-66} Test statistic Computed : as The t- statistic follows is to X-Mo sloni a trai Under Ho 22.3-25.3 t8.31100 =) = -3.614 | Decision about the null Hypothesis Since it is observed that, t-Calculated value t=-3.614 which is less than the tacritical value ta 1.66 cs Scanned with CamScanner

That is t - Statistic < t - Critical -3.614 < -1.66 It is then . concluded that the hall hypothesis is rejected. using the P-value approach from tables the P-value is P=0.000 2, . and since P=0.0002 < 2:0.05 it is concluded that the null hypotheses is rejected. Conclusion: It is concluded the hull hybolhesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean M is less than 25.3 at 0.05 Significance level 2 Scanned with CamScanner

The e value is a number between o and I A and interpreted, A small p-value (ie pco.os) indicates strong evidence against the hull hypothesis so you reject the null hypothesis In this Problem the P-valle is 0.0002 which is less than 0.05 . It indicates strong evidence againy the hull hypothesis, so we reject the hall hypothesis Ho. Scanned with CamScanner