Question

I keep getting the wrong answer, so maybe I'm just doing my math wrong, anyway an someone help me out?

Answer 1

A bank wants to get new customers for their credit card. They try two different approaches in their marketing campaign. The first promises a "cash back" reward; the second promises low interest rates. A sample of 500 people is mailed the first brochure; of these, 100 get the credit card. A separate sample of 500 people is mailed the second brochure; 125 get the credit card. Are the two campaigns equally attractive to customers? Compute a 95% confidence interval for the difference in the two proportions.
A. (0.21, 0.29)
B. (–0.102, 0.002)
C. (-0.118, 0.018)

Answer 2

what did you get for the critical z value?

Answer 3

95% = z* of 1.960

Answer 4

close enough

Answer 5

now we need to compute phat1

phat1 = x1/n1

phat1 = 100/500

phat1 = 0.2

Answer 6

qhat1 = 1 - phat1

qhat1 = 1 - 0.2

qhat1 = 0.8

Answer 7

the same is done for phat2 and qhat2

phat2 = x2/n2

phat2 = 125/500

phat2 = 0.25


qhat2 = 1 - phat2

qhat2 = 1 - 0.25

qhat2 = 0.75

Answer 8

Ok, I redid it, and I got B, did you get that answer as well?

Answer 9

Now we use this to calculate the 95% Confidence Interval (CI)



Lower Limit:



L = (phat1-phat2)-z*sqrt( (phat1*qhat1)/n1 + (phat2*qhat2)/n2 )



L = (0.2-0.25)-1.96*sqrt( (0.2*0.8)/500 + (0.25*0.75)/500 )



L = -0.10167119119973



L = -0.102



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



Upper Limit:



U = (phat1-phat2)+z*sqrt( (phat1*qhat1)/n1 + (phat2*qhat2)/n2 )



U = (0.2-0.25)+1.96*sqrt( (0.2*0.8)/500 + (0.25*0.75)/500 )



U = 0.00167119119973



U = 0.002



The 95% confidence interval is (L, U) = ( -0.102, 0.002 )

Answer 10

yep, got B

Answer 11

Great! Thanks!

Answer 12

np