Question

Exhibit 8 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type Pop Rap Teenagers Surveyed 710 Teenagers Favoring This Type 394 460 990 Refer to Exhibit 10-12. The 98% confidence interval for the difference between the two proportions is Select one: a. 0.498 to 2.6585 5.0.0333 to 1472 c0.0328 to 1.268 d. 0.2384 to 1.6450

Answer 1

We know that the 98% confidence interval for difference of proportions is given by:

$[(\widehat{p_{1}}-\widehat{p_{2}})\pm Z_{0.02/2}\sqrt{\frac{\widehat{p_{1}}(1-\widehat{p_{1}})}{n_{1}}+\frac{\widehat{p_{2}}(1-\widehat{p_{2}})}{n_{2}}}]$

$[(\frac{394}{710}-\frac{460}{990})\pm Z_{0.01}\sqrt{\frac{\frac{394}{710}(1-\frac{394}{710})}{710}+\frac{\frac{460}{990}(1-\frac{460}{990})}{990}}]$

$[(\frac{394}{710}-\frac{460}{990})\pm (2.3263)\sqrt{\frac{\frac{394}{710}(1-\frac{394}{710})}{710}+\frac{\frac{460}{990}(1-\frac{460}{990})}{990}}]$

$[(0.0903)\pm 0.0569]$

Hence option B is the correct option.