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.

To answer this question, we will follow the steps provided:

A. Constructing a 95% Confidence Interval:
We can use the formula for the confidence interval of the difference between two proportions:

CI = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where:
- p1 is the proportion of high-school students who read newspapers regularly,
- p2 is the proportion of college students who read newspapers regularly,
- n1 is the sample size of high-school students, and
- n2 is the sample size of college students.

In this case, p1 = 287/500 = 0.574 and p2 = 252/420 = 0.6.
The sample sizes are n1 = 500 and n2 = 420.

To satisfy the conditions for using a z-interval, the following conditions need to be met:
1. Both samples are random and representative of their respective populations.
2. The distribution of each sample proportion is approximately normal. Since the sample sizes are large enough (both n1 and n2 are greater than or equal to 30), we can assume this condition is satisfied.
3. The samples are independent of each other, meaning that the response of one student does not influence the response of another.

Once we have confirmed that the conditions are satisfied, we can plug in the values into the confidence interval formula and calculate the interval.

B. Drawing a conclusion:
Based on the calculated 95% confidence interval, we can conclude that we are 95% confident that the true difference between the proportions of high-school students and college students who read newspapers regularly lies within the interval we calculated. The result will be a range of values that represents the likely difference between the two proportions.

C. Null and alternative hypothesis:
To conduct a significance test, we need to define the null and alternative hypotheses. In this case, we want to determine if the proportion of high-school students who read newspapers regularly is significantly lower than the proportion of college students.

Null hypothesis (H0): The proportion of high-school students who read newspapers regularly is equal to the proportion of college students.
Alternative hypothesis (Ha): The proportion of high-school students who read newspapers regularly is less than the proportion of college students.

D. Calculating p-hat, the pooled estimate of the population proportions:
The pooled estimate of the population proportions (p-hat) is calculated by combining the proportions of both samples weighted by their respective sample sizes:

p-hat = (p1 * n1 + p2 * n2) / (n1 + n2)

Substituting the given values, p-hat = (0.574 * 500 + 0.6 * 420) / (500 + 420).

E. Demonstrating the requirements for using a z-procedure:
For the z-procedure to be appropriate, the following requirements should be met:
1. The sampling distribution of the difference between the two proportions (p1 - p2) is approximately normal - We can assume this condition is satisfied since both sample sizes are large enough (500 and 420).
2. The samples are independent - Since the samples are from different populations, we assume independence.
3. Randomization condition - The samples are described as random samples, which satisfies this condition.

Once all these conditions have been met, we can proceed with using the z-procedure for conducting the significance test about the difference between two proportions.

Remember that conducting a significance test would involve calculating the test statistic, determining the critical value or p-value, and comparing it to the significance level to make a decision.