Hello,

This is the first time I've had to get homework help. This is a tough one for me, if I could get some help please?

• Analyze the impact the new protocol (PE) has had on time in queue and service time.
• Determine if the PE protocol should be implemented widely in the call center with what you know so far.
• Identify what additional data and analyses would be helpful to determine if the PE protocol is working.
• Explain what is likely to happen to TiQ and ST if the PT protocol is kept.
• Explain how a sudden increase of 20% more calls might influence TiQ and ST.
• Justify whether the data is sufficient to determine if the PE test is successful.
• Suggest additional metrics and supporting data needed to determine the performance of the call center's operations.

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 =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 : < 150

This is a left-tailed test, and with a significance level of =0.05 the critical value is z = -1.645. The decision rule becomes: Reject Ho if z_calc < -1.645.

Figure 1: TiQ Rejection Region

The test statistic is given by:

The test statistic z_calc falls outside the rejection region, so we do not reject the null hypothesis in favor of the alternate hypothesis. We conclude the call center's average TiQ is greater than the industry's average of 150 seconds.

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 =0.05 was used.

This is a test of means for two independent samples with unknown variances assumed unequal.

Sample 1 is the data from the PE (new) protocol. Sample 2 is the data from the PT (current) protocol. We tested whether the mean ST with protocol PE is smaller than the mean with protocol PT (we align the research question with the alternative hypothesis test.

The null and alternate hypotheses are:

Ho : 1 > 2

H1 : 1 < 2

This is a left-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 =0.05 is t = -1.645.

The decision rule becomes: Reject Ho if t_calc < -1.645.

Figure 3: Hypothesis Test of Independent Groups (t-test, unequal variance)

The t_calc = -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.