Question

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 was mailed the first brochure; of these, 100 get the credit card. A separate sample of 500 people was mailed the second brochure; 125 get the credit card. Are the two campaigns equally attractive to customers? Find the test statistic. And compute a 95% confidence interval for the difference between the two proportions

Answer 1

(-0.1018, 0.0018)

Explanation:

Given that 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 was mailed the first brochure; of these, 100 get the credit card. A separate sample of 500 people was mailed the second brochure; 125 get the credit card.

i.e. p1 =
`100/500 = 0.2`

p2 =
`125/500 = 0.25`

p difference =
`-0.05`

Combined p =
`(100+125)/(500+500) \\=0.225`

1-p = 0.775

Std error for difference =
`\sqrt{0.225*0.775)((1)/(500) +(1)/(500)} )\\=0.02641`

Margin of error for 95%

=1.96 * std error = 0.0518

Confidence interval for differnce =

`(-0.05-0.0518, -0.05+0.0518)\\= (-0.1018, 0.0018)`