Question

A recent report suggests that Chief Information Officers (CIO's) who report directly to Chief Financial Officers (CFO's) rather than Chief Executive Officers (CEO's) are more likely to have IT agendas that deal with cost cutting and compliance. In a random sample of 843 companies, it was found that CIO's reported directly toCFO's in 169 out of 524 service firms and in 107 out of 319 manufacturing companies.

Give a 95​% confidence interval for the difference p1−p2​, where p1 and p2 are the proportions of​ CIO's who report directly to the CFO in service firms and manufacturing​ companies, respectively.

The 95​% confidence interval is ( ____ , ____ )

​(Round to three decimal places as needed. Use ascending​ order.)

Answer 1

solution:

p1=169/524=0.3225

p2=107/319=0.3354

Pooled proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)

=(0.3225*524+0.3354*319)/843  

=(168.99+106.99)/843

=0.3273

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

=sqrt(0.3273*0.6726)*1/524+1/319)

=0.0333

95 %confidence interval the critical value is 1.96

=p1 - p2 +/- zc * SE

=(0.3225-0.3354)+/-1.96*0.0333

=(-0.0129+/-0.065268)

=(-0.0781,0.0523)