A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for (pcollege grad - pHS or less)? where p 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.52 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. 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. 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%. A 90% confidence interval for (pcollege grad - pHS or less) would be wider. A 95% confidence interval for (pHS or less - Pcollege grad) is (-0.15,-0.07).

The true statements include

- 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.

- A 95% confidence interval for (pHS or less - Pcollege grad) is (-0.15,-0.07).

The false statements include

- 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.

- 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%

- A 90% confidence interval for (pcollege grad - pHS or less) would be wider.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

For this question, note that the resulting distribution whose sample proportion is a difference between college grad and an highschool ,

Sample proportion = (pcollege grad - pHS or less)?

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for such a large sample size is obtained from the z-tables.

Critical value = 1.960

So, when using the confidence interval to compare two distributions and the resulting distribution is the difference in the proportions of those two quantities being compared, if the confidence interval contains 0, it means that there isn't a difference between the two entities being compared

Taking the statements provided one at a time.

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.

Since the confidence interval obtained does not contain a 0 in the confidence interval obtained, it shows that there really is a significant difference between the proportns being considered. Hence, this statement is true.

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.

This isn't true according to the definition of confidence interval. The right point is that we are 95% confident that more than 7% to less than 15% more college graduates watch The Daily Show than those with a high school degree or less. This statement 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 differences in sample proportions between 7% and 15%.

This is nowhere near the definition of a confidence interval. A confidence interval is used to obtain population proportion, not more sample proportions. Hence, this statement is false.

4) A 90% confidence interval for (pcollege grad - pHS or less) would be wider.

The confidence interval depends mostly on the margin of error which is then in turn, directly proportional to the critical value, which is obtained based on z-tables.

The critical value increases as the confidence level increases, hence, 90% confidence interval cannot be wider than 95% confidence interval.

This statement is not true.

5) A 95% confidence interval for (pHS or less - Pcollege grad) is (-0.15,-0.07).

This just reverses the sign on the resulting sample proportion uses to calculate the confidence interval, hence, this is correct.

Hope this Helps!!

f is the midpoint of