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Homework answers / question archive / A recent report suggests that Chief Information Officers(CIO's) who report directly to Chief Financial Officers (CFOs) rather than Chief Executive Officers(CEOs) are more likely to have IT agendas that deal with cost cutting and compliance
A recent report suggests that Chief Information Officers(CIO's) who report directly to Chief Financial Officers (CFOs) rather than Chief Executive Officers(CEOs) are more likely to have IT agendas that deal with cost cutting and compliance. In a random sample of 535 companies, it was found that CIOs reported directly to CFOs in 173 out of 335 service firms and in 95 out of 200 manufacturing companies.
A) Is there evidence that type of business(service versus manufacturing) and whether or not the CIO reports directly to the CFO are associated?
B) If your conclusion proves to be wrong, did you make a Type 1 or type 2 error?
C) Give a 95% confidence interval for the difference in proportions of companies in which the CIO reports directly to the CFO between service an dmanufacturing firms.
Answer:
|
Z Test for Differences in Two Proportions |
|
|
Data |
|
|
Hypothesized Difference |
0 |
|
Level of Significance |
0.05 |
|
Group 1 |
|
|
Number of Items of Interest |
173 |
|
Sample Size |
335 |
|
Group 2 |
|
|
Number of Items of Interest |
95 |
|
Sample Size |
200 |
|
Intermediate Calculations |
|
|
Group 1 Proportion |
0.5164 |
|
Group 2 Proportion |
0.4750 |
|
Difference in Two Proportions |
0.0414 |
|
Average Proportion |
0.5009 |
|
Z Test Statistic |
0.9270 |
|
Two-Tail Test |
|
|
Lower Critical Value |
-1.9600 |
|
Upper Critical Value |
1.9600 |
|
p-Value |
0.3539 |
|
Do not reject the null hypothesis |
|
Calculated Z=0.927 which is not in the rejection region
The null hypothesis is not rejected.
There is no evidence that type of business(service versus manufacturing) and whether or not the CIO reports directly to the CFO are associated.
If our conclusion of there is no difference proves to be wrong, we made a type 2 error.
C) Give a 95% confidence interval for the difference in proportions of companies in which the CIO reports directly to the CFO between service an dmanufacturing firms.
|
Confidence Interval Estimate |
|
|
of the Difference Between Two Proportions |
|
|
Data |
|
|
Confidence Level |
95% |
|
Intermediate Calculations |
|
|
Z Value |
1.9600 |
|
Std. Error of the Diff. between two Proportions |
0.0446 |
|
Interval Half Width |
0.0875 |
|
Confidence Interval |
|
|
Interval Lower Limit |
-0.0461 |
|
Interval Upper Limit |
0.1289 |
PFA
