SOLUTION: A 20 minute consumer survey mailed to 500 adults aged 25-34 included a $5 Starbucks gift certificate.The same survey was mailed to 500 adults aged 25-34 without the gift certificat

Question 135555This question is from textbook
: A 20 minute consumer survey mailed to 500 adults aged 25-34 included a $5 Starbucks gift certificate.The same survey was mailed to 500 adults aged 25-34 without the gift certificate. There were 65 responses from the first group and 45 from the second group.(a)Perform a two tailed test comparing the response rates(proportions)at ∝ = .05. (b) Form a confidence interval for the difference of proportions, without pooling the samples. Does it include zero?
This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A 20 minute consumer survey mailed to 500 adults aged 25-34 included a $5 Starbucks gift certificate.The same survey was mailed to 500 adults aged 25-34 without the gift certificate. There were 65 responses from the first group and 45 from the second group.
(a)Perform a two tailed test comparing the response rates(proportions)at ∝ = .05.
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p-hat with certificate = 65/500 = 0.13
p-hat no certificate = 45/500 = 0.09
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Ho: p-hats difference = 0
Ha: p-hats no difference
Pooled: p-bar = (65+45)/1000 = 110/1000 = 0.11
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Crit value: z = +/- 1.96
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Test Stat: z(0.13-0.09) = (0.04-0)/sqrt[(0.11)(0.89)/500 + (0.11)(0.89)/500]
= 0.04/0.019789 = 2.02
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Conclusion: Test stat is greater than crit value so Reject Ho.
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(b) Form a confidence interval for the difference of proportions, without pooling the samples. p-hat(diff)=(0.13-0.09)
E = 1.96sqrt[(0.13)(0.87)/500 + (0.09)(0.91)/500] = 1.96*0.019748=0.03871
CI: 0.04-0.03871 < p < 0.04+0.03871
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Does it include zero? No
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Cheers,
Stan H.

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