Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected
-A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval
For the difference between the two population proportions.
A) $- 0.0034

Question

Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected
-A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval
For the difference between the two population proportions. 
A) $- 0.0034 < \mathrm { p } 1 - \mathrm { p } 2 < 0.0566$
B) $0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286$
C) $- 0.0177 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.1243$
D) $- 0.0443 < \mathrm { p } 1 - \mathrm { p } _ { 2 } < 0.0976$

Quizplus · Accepted Answer

We use the formula for the confidence interval for the difference between two population proportions:

$\mathrm{(\hat{p_1} - \hat{p_2}) \pm z* \sqrt{\frac{\hat{p_1}(1-\hat{p_1})}{n_1} + \frac{\hat{p_2}(1-\hat{p_2})}{n_2}}}$

Where $\mathrm{\hat{p_1}}$ is the sample proportion of New Yorkers who knew the product (193/558 = 0.345), $\mathrm{\hat{p_2}}$ is the sample proportion of Californians who knew the product (196/614 = 0.319), $\mathrm{n_1}=558$, $\mathrm{n_2}=614$, and z is the z-score for a 99% confidence interval, which is 2.576.

Plugging in the values, we get:

$(-0.0443) < \mathrm{(\hat{p_1} - \hat{p_2})} < 0.0976$

Therefore, the best choice is D, $-0.0443 < \mathrm{p_1-p_2} < 0.0976$

Write the Word or Phrase That Best Completes Each Statement −0.0034<p1−p2<0.0566- 0.0034 < \mathrm { p } 1 - \mathrm { p } 2 < 0.0566−0.0034<p1−p2<0.0566

Write the Word or Phrase That Best Completes Each Statement $- 0.0034 < \mathrm { p } 1 - \mathrm { p } 2 < 0.0566$