Question

The Daily Show. A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, of the 1,110 people in the poll with a high school degree but no college degree, 22% watch The Daily Show. A 95% confidence interval for pCollegeGrad−pHighSchoolpCollegeGrad−pHighSchool, where pp is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false.

1. At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show.  ? True False

2. We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less.  ? True False

3. 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield differences in sample proportions between 7% and 15%.  ? True False

4. 90% confidence interval for pCollegeGrad−pHighSchoolpCollegeGrad−pHighSchool would be wider.  ? True False

5. A 95% confidence interval for pHighSchool−pCollegeGradpHighSchool−pCollegeGrad is (-0.15,-0.07).  ? True False

Answer 1

1:

Since confidence interval does not contain zero so we the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show at 5% level of significance.

Answer: It is true.

2:

We are 95% confident that between 7% to 15% more college graduates watch The Daily Show than those with a high school degree or less.  

Answer:It is False

3:

. 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield true differences between confidence interval.

Answer:It is False

4:

No 90% confidence interval for pCollegeGrad−pHighSchoolpCollegeGrad−pHighSchool would be narrower.

Answer:It is False

5;

Answer: It is true.