University of Phoenix Call Time Analysis Time in Queue Test The team performed a test of hypothesis to determine whether the average TiQ is lower than the industry standard of 2.5 minutes (150 seconds). A significance level a=0.05 was used. This was a test of mean against a hypothesized value of 150 seconds. Because the sample size was large, we assumed knowledge of the population's variance. The null and alternate hypotheses is: Ho: 150 H1: 2 This is a right-tailed test. Because of the very large samples, there is no real difference between finding the critical value with a normal distribution or the t distribution. The critical value with a significance level a=0.05 is t = 1.645. The decision rule becomes: Reject Ho if tcalc > 1.645. Figure 2: Results of TIQ Hypothesis Test: Mean versus Hypothesized Value Average Service Time Test The team performed a test of hypothesis to determine whether the service time (ST) with new service protocol PE is lower than with the current PT protocol. A significance level of a=0.05 was used. This is a test of means for two independent samples with unknown variances assumed unequal. Hypothesis Test: Independent Groups (t-test, unequal variance) PE Protocol 149.28 185.89 853 PT Protocol 212.16 mean 190.58 std. dev. 821 n 1665 df -62.883 difference (PE Protocol - PT Protocol) 9.206 standard error of difference 0 hypothesized difference -6.831 t 5.91E-12 p-value (one-tailed, lower) -80.940 confidence interval 95.% lower -44.826 confidence interval 95.% upper 18.057 margin of error Figure 3: Hypothesis Test of Independent Groups (t-test, unequal variance) The tcalc = -6.8 falls in the rejection region. We conclude that the new protocol (PE) results in a shorter average service time than the traditional protocol (PT) based on available data. End of document