You want to know if there's a difference between the proportions of high school students and college students who read newspapers regularly. out of a random sample of 500 high-school students, 287 say they read newspapers regularly, and out of a random sample of 420 college students, 252 say they read newspapers regularly. for this question, think of high-school students as sample one and college students as sample two.

A. Construct a 95% confidence interval for the difference between the proportions of high-school students and college students who read newspapers regularly. be sure to show that you've satisfied the conditions for using a z-interval.
B. draw a conclusion, based on your 95% confidence interval about the difference between the two proportions.
C. if you wanted to use a test statistic to determine whether the proportion of high school students who read newspapers regularly is significantly lower than the proportion of college students who read newspapers regularly, what would you use as your null and alternative hypothesis?
D. calculate p-hat, the pooled estimate of the population proportions you'd use for a significance test about the difference between the proportions of high school students and college students who read newspapers regularly.
E. Demonstrate that these samples meet the requirements for using a z-procedure for a significance test about the difference between two proportions.
F. Calculate SE(p-hat), the pooled estimate of the standard errors of the proportions you'd used in a z-procedure for a significance test about the difference between two proportions.
G. Calculate your test statistic and P-value for the hypothesis test Ho:p1=p2, Ha: p1<p2.
H. draw a conclusion about the difference between the two proportions using alpha=0.05. is the proportion of high-school students who read the newspapers on a regular basis less than the proportion of college students who read newspapers regularly?

A. To construct a 95% confidence interval for the difference between the proportions of high school students and college students who read newspapers regularly, we need to satisfy the conditions for using a z-interval.

The conditions for using a z-interval are:
1. Randomization: The samples should be randomly selected from the populations of high school and college students.
2. Independence: The two samples should be independent, meaning one sample does not affect the other.
3. Normality: The number of successes and failures in each sample should be at least 10.

Based on the information given, the conditions are likely satisfied, as the samples were randomly selected, assumed to be independent, and the number of successes and failures in each sample is greater than 10.

B. To draw a conclusion based on the 95% confidence interval, we need to check if the interval includes zero. If the interval includes zero, it suggests that there is not a significant difference between the proportions. If the interval does not include zero, it suggests that there is a significant difference between the proportions.

C. The null and alternative hypothesis for the test statistic would be:
Null Hypothesis (Ho): The proportion of high school students who read newspapers regularly is not significantly lower than the proportion of college students who read newspapers regularly.
Alternative Hypothesis (Ha): The proportion of high school students who read newspapers regularly is significantly lower than the proportion of college students who read newspapers regularly.

D. To calculate p-hat, the pooled estimate of the population proportions, we add the number of successes from both samples and divide by the total number of observations. In this case, p-hat would be (287 + 252) / (500 + 420).

E. To demonstrate that the samples meet the requirements for using a z-procedure, we need to check if the number of successes and failures in each sample is at least 10, which was already satisfied in the given information.

F. To calculate SE(p-hat), the pooled estimate of the standard errors of the proportions, we use the formula:
SE(p-hat) = sqrt((p-hat1 * (1 - p-hat1) / n1) + (p-hat2 * (1 - p-hat2) / n2))
Here, p-hat1 and p-hat2 are the sample proportions, and n1 and n2 are the sample sizes.

G. To calculate the test statistic and p-value for the hypothesis test, we use the formula for a two-sample z-test:
Test Statistic = (p-hat1 - p-hat2) / SE(p-hat)
P-value = P(Z < test statistic), where Z is the standard normal distribution.

H. Based on the calculated test statistic and p-value, and using a significance level of 0.05, we can make a conclusion about the difference between the two proportions. If the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis, which would suggest that the proportion of high-school students who read newspapers regularly is less than the proportion of college students. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis, indicating insufficient evidence to suggest a significant difference in proportions.