In a recent year, it was reported that the mean wait for repairs for a phone com

ID: 3131234 • Letter: I

Question

In a recent year, it was reported that the mean wait for repairs for a phone company's customers was 34.5 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 30.3 hours and a sample standard deviation of 10.7 hours. Complete parts (a) and (b) below. Click to view the first page of the table of critical values of t. Click to view the second page of the table of critical values of t. Is there evidence that the population mean amount is less than 34.5 hours? (Use a 0.05 level of significance.) State the null and alternative hypotheses. Find the test statistic for this hypothesis test. The critical value(s) of the test statistic is(are) . (Round to four decimal places as needed. Use a comma to separate answers as needed.)

Explanation / Answer

Solution:

We are given,

Sample size = n = 100

Population mean = 34.5

Sample mean = 30.3

Sample standard deviation = 10.7

Level of significance = alpha = = 0.05

Here, we have to use the one sample t test for the population mean which is given as below:

t Test for Hypothesis of the Mean

Data

Null Hypothesis m=

34.5

Level of Significance

0.05

Sample Size

100

Sample Mean

30.3

Sample Standard Deviation

10.7

Intermediate Calculations

Standard Error of the Mean

1.0700

Degrees of Freedom

t Test Statistic

-3.9252

Lower-Tail Test

Lower Critical Value

-1.6604

p-Value

0.0001

Reject the null hypothesis