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# Hypothesis Testing

Problems are attached in word format. The questions are posted below to provide quicker review. Thanks,

Q1) Does gender impact the use of electronic mail (e-mail)? An insurance company studied the use of e-mail in its organization by counting the number of business-related e-mails generated by 10 men and 10 women matched on job position in a day. The data are below:

Men Women
82 48
77 61
78 56
83 59
82 58
78 56
81 60
74 64
86 59
76 53

a) Calculate the differences in the number of business-related e-mails for each male/female pair. Just looking at the differences, do you think that men use e-mail more? Why or why not?

b) Calculate the average differences and the standard deviation of the differences.

c) Set up the hypotheses to test whether the average number of business-related e-mails generated by men is greater than that generated by women.

d) Assuming that the data are normally distributed, at the 0.05 level of significance, what can you conclude?

Q2) It has been a widely held belief that the switch to participative management would increase employees' buy-in to the company. One of the benefits that should be realized is a reduction in the number of sick days that employees use. A company that has made the switch in some departments wonders if this has been true. It decides to sample 25 employees from each of two manufacturing departments. The first has been using a participative management style for almost two years and the second is still using a traditional management style. The data on the number of sick days used by each employee in the past 12 months are found below:

1 3 5 5 6 0 5 6 7 9
1 4 5 6 7 3 5 7 7 9
2 4 5 6 8 4 6 7 7 10
2 4 5 6 8 4 6 7 8 11
3 4 5 6 8 5 6 7 8 11

At the 0.05 level of significance, does the data provide enough evidence to say that employees who sue participative management styles use, on the average, fewer sick days than those who use traditional management style? Be sure to justify any assumptions you make in selecting the test procedure you use.

Q3)
The software company that is looking at the time to failure of the diskettes (hours) it uses decides to look at an alternative supplier of the product. The data for the current supplier and for the new supplier are shown below:

Current Supplier Alternative Supplier
486 494 502 508 489 492 495 498
490 496 504 510 489 492 496 499
491 498 505 514 491 493 497 502
491 498 506 515 492 493 497 503
494 498 507 527 492 494 497 505

The company has decided that if the mean time to failure for the new supplier is longer than it is from the current supplier, it will switch suppliers.

a) What level of significance would you suggest the company use? justify your choice.

b) Assuming that the data are normally distributed, should the company switch suppliers? Use the level of significance you chose in part (a).

c) What impact did your choice of a have on the decision?

#### Solution Preview

if you can't read it clearly, please refer to the attached WORD and EXCEL files.
<br>
<br>Q1)a) Calculate the differences in the number of business-related e-mails for each male/female pair. Just looking at the differences, do you think that men use e-mail more? Why or why not?
<br>
<br>The difference (D) = the number of e-mails for each male - the number of e-mails for each female (please refer to the attached EXCEL file for calculation)
<br>And we can find from the table that all D's are relatively large positive values, which intuitively means that men use e-mail more.
<br>
<br>b) Calculate the average differences and the standard deviation of the differences.
<br>
<br>please refer to the attached EXCEL file for calculation:
<br>average difference is Md=SUM(D)/10=22.3
<br>and standard deviation is Sd= SQRT{SUM[(D-Md)^2]/(10-1)}=6.308
<br>
<br>c) Set up the hypotheses to test whether the average number of business-related e-mails generated by men is greater than that generated by women.
<br>
<br>Ho: Md=0 (average number of e-mails is the same for men and women.)
<br>H1: Md>0 (average number of e-mails by men is greater than that by women.)
<br>
<br>d) Assuming that the data are normally distributed, at the 0.05 level of significance, what can you conclude?
<br>
<br>We use one-tailed t-test, using significance level a=0.05, and df=10-1=9
<br>So ...

#### Solution Summary

Problems are attached in word format. The questions are posted below to provide quicker review. Thanks,

Q1) Does gender impact the use of electronic mail (e-mail)? An insurance company studied the use of e-mail in its organization by counting the number of business-related e-mails generated by 10 men and 10 women matched on job position in a day. The data are below:

Men Women
82 48
77 61
78 56
83 59
82 58
78 56
81 60
74 64
86 59
76 53

a) Calculate the differences in the number of business-related e-mails for each male/female pair. Just looking at the differences, do you think that men use e-mail more? Why or why not?

b) Calculate the average differences and the standard deviation of the differences.

c) Set up the hypotheses to test whether the average number of business-related e-mails generated by men is greater than that generated by women.

d) Assuming that the data are normally distributed, at the 0.05 level of significance, what can you conclude?

Q2) It has been a widely held belief that the switch to participative management would increase employees' buy-in to the company. One of the benefits that should be realized is a reduction in the number of sick days that employees use. A company that has made the switch in some departments wonders if this has been true. It decides to sample 25 employees from each of two manufacturing departments. The first has been using a participative management style for almost two years and the second is still using a traditional management style. The data on the number of sick days used by each employee in the past 12 months are found below:

1 3 5 5 6 0 5 6 7 9
1 4 5 6 7 3 5 7 7 9
2 4 5 6 8 4 6 7 7 10
2 4 5 6 8 4 6 7 8 11
3 4 5 6 8 5 6 7 8 11

At the 0.05 level of significance, does the data provide enough evidence to say that employees who sue participative management styles use, on the average, fewer sick days than those who use traditional management style? Be sure to justify any assumptions you make in selecting the test procedure you use.

Q3)
The software company that is looking at the time to failure of the diskettes (hours) it uses decides to look at an alternative supplier of the product. The data for the current supplier and for the new supplier are shown below:

Current Supplier Alternative Supplier
486 494 502 508 489 492 495 498
490 496 504 510 489 492 496 499
491 498 505 514 491 493 497 502
491 498 506 515 492 493 497 503
494 498 507 527 492 494 497 505

The company has decided that if the mean time to failure for the new supplier is longer than it is from the current supplier, it will switch suppliers.

a) What level of significance would you suggest the company use? justify your choice.

b) Assuming that the data are normally distributed, should the company switch suppliers? Use the level of significance you chose in part (a).

c) What impact did your choice of a have on the decision?

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