Question

A telemarketing company based in Utah has established a guideline stating that the average time for each completed call should be no more than 250 seconds. Recently the operations manager was concerned that calls were taking too long. The operations manager did not wish to assert that the calls were taking too long if the sample data did not strongly indicate this.

A sample of 12 calls was selected and the following times (in seconds) were recorded. 194 278 302 140 245 234 268 208 302 190 320 255

Based on the sample data, develop appropriate null and alternate hypothesis and perform the relevant hypothesis test. Test the hypothesis at the 0.10 significance level using the pvalue approach. (Assume that call times are normally distributed.). You are NOT allowed to use PHStat4 to answer this question. Report your results using 7-step method discussed in the class.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 250
Alternative Hypothesis, Ha: μ < 250

Rejection Region
This is left tailed test, for α = 0.1 and df = 11
Critical value of t is -1.363.
Hence reject H0 if t < -1.363

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (244.67 - 250)/(53.92/sqrt(12))
t = -0.342

P-value Approach
P-value = 0.3694
As P-value >= 0.1, fail to reject null hypothesis.

Sample indicates that the call length is not too long