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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

Respuesta :

Answer:

(-0.1018, 0.0018)

Step-by-step 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 = [tex]100/500 = 0.2[/tex]

p2 = [tex]125/500 = 0.25[/tex]

p difference = [tex]-0.05[/tex]

Combined p = [tex]\frac{100+125}{500+500} \\=0.225[/tex]

1-p = 0.775

Std error for difference = [tex]\sqrt{0.225*0.775)(\frac{1}{500} +\frac{1}{500}} )\\=0.02641[/tex]

Margin of error for 95%

=1.96 * std error = 0.0518

Confidence interval for differnce =

[tex](-0.05-0.0518, -0.05+0.0518)\\= (-0.1018, 0.0018)[/tex]

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