"A recent report suggests that Chief Information Officers(CIO's) who report directly to Chief Financial Officers (CFOs)"

Question

"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."

Accepted Answer

"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 Is there evidence that type of business(service versus manufacturing) and whether or not the CIO reports directly to the CFO are associated? 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 your conclusion proves to be wrong, did you make a Type 1 or type 2 error? 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"

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

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

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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

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