Question

A Telecommunications company recently installed a new speech recognition system for its repair calls. In their old system, operators had to press keys on the numeric keypad to answer questions, which led to longer time on service calls. on service calls. The company is conducting a study to examine the impact of the new system on the average duration of service calls. Average duration of service calls was 31.4 minutes prior to the installation of the new system. They analyzed a random sample of 20 service calls and obtained an average duration of service calls of 29.4 minutes. Based on historical data, the standard deviation of duration of service calls is known to be σ =6.2 minutes.

What is the P value of the the hypothesis test to determine if the system has been effective reducing the average duration of service calls ? (Use 4 DECIMALS)

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 31.4
Alternative hypothesis: u < 31.4

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.3864
DF = n - 1

D.F = 19
t = (x - u) / SE

t = - 1.44

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesised population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.44.

Thus the P-value in this analysis is 0.0831.

Interpret results. Since the P-value (0.0831) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the system has been effective reducing the average duration of service calls.