You\'ve been hired as the manager at a digital marketing company in town that is

Question

You've been hired as the manager at a digital marketing company in town that is undergoing significant reorganization. Their profits are down and you have determined that two separate teams employed there do essentially the same job. Due to time constraints and space needs, the most fair way to downsize is to cut an entire team rather than evaluate each employee individually. Below are the productivity scores (on a scale from 1-100) for each team member and customer satisfaction ratings (0-100%) for interactions with each employee on each team. Using only productivity scores, report the t-statistic for this comparison. Show all work and report in full APA style with df and p value ( 0.05). Use a two-tailed alpha level at 0.05. Do productivity scores along give you adequate data to decide which team should get fired? What is your decision and why? Now consider customer satisfaction ratings. Report the t-statistic for this comparison. Show all work and report in full APA style with df and p value ( 0.05). Use a two-tailed alpha level at 0.05. Could this data change your decision? How? Which team gets fired?

Explanation / Answer

a) Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean for team1 (productivity score).

mu2 is population mean for team2 (productivity score)

Assume alpha = 5% = 0.05

First we have to test whether variances are equal or not.

H0 : variances are equal.

H1 : Variances are not equal.

We can test variances by using F-test.

We can done all these testing by using EXCEL.

steps :

Enter all data in EXCEL sheet --> Data --> Data Analysis -->F-Tesr Two-Sample for Variances --> ok --> Variable 1 Range : select team1 range --> Variable 2 Range : select team 2 range --> Alpha : 0.05 --> Output Range : select any one empty cell --> ok

Output :

Test statistic F = 0.4405

P-value = 0.17

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Two variances are equal.

So we use pooled variances.

Two sample t-test in EXCEL:

Data --> Data Analysis --> t-Test:Two-Sample Assuming Equal Variances --> ok --> Variable 1 Range : select team1 range --> Variable 2 Range : select team 2 range --> Alpha : 0.05 --> Output Range : select any one empty cell --> ok

Output is :

Test statistic t = -1.011

P-value = 0.33

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Two population means are equal.

--------------------------------------------------------------------------------------------------------------------------------------------------------------

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean for team1 (customer satisfaction).

mu2 is population mean for team2 (customer satisfaction)

Assume alpha = 5% = 0.05

First we have to test whether variances are equal or not.

H0 : variances are equal.

H1 : Variances are not equal.

We can test variances by using F-test.

We done all the testing in EXCEL in similar way.

Results are :

Test statistic F = 1.333

P-value = 0.368

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Variances are equal.

So we use pooled variances.

Test statistic t = 1.546

P-value = 0.1480

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Two population means are equal.

F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 39.28571 53.71429 Variance 435.9048 989.5714 Observations 7 7 df 6 6 F 0.440499 P(F<=f) one-tail 0.170832 F Critical one-tail 0.233434

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