I need help with 2 questions-TODAY-HELP

8. Assume that the MM207 Student Data Set is a random sample of all Kaplan students; estimate the proportion of all Kaplan students who are male using a 90% level of confidence.

9. Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need?

To answer the first question:

To calculate the proportion of all Kaplan students who are male using a 90% level of confidence, you will need to follow these steps:

1. Take a random sample: You need to have a sample of students from the MM207 Student Data Set. Ensure that the sample is random and representative of all Kaplan students.

2. Count the number of male students: Within your random sample, determine how many students are classified as male.

3. Determine the sample size: Note the size of your sample (total number of students) from the MM207 Student Data Set.

4. Calculate the sample proportion: Divide the number of male students by the total sample size to get the sample proportion of male students in the dataset.

5. Determine the confidence level: The question mentions a 90% level of confidence. This means you want to be 90% confident that your estimate falls within the confidence interval.

6. Find the critical value: Determine the critical value associated with the desired confidence level. For a 90% level of confidence, the critical value is 1.645.

7. Calculate the margin of error: Multiply the critical value by the standard error. The standard error can be calculated by taking the square root of (sample proportion * (1 - sample proportion) / sample size).

8. Calculate the confidence interval: Subtract the margin of error from the sample proportion to find the lower bound, and add the margin of error to the sample proportion to find the upper bound. This will give you the range within which the true proportion of male students lies with 90% confidence.

To answer the second question:

To estimate the sample size required when you want to estimate the proportion of students who commute less than 5 miles to work within a 2% margin of error, you can follow these steps:

1. Determine the desired margin of error: In this case, it is given as 2%.

2. Determine the confidence level: Determine the level of confidence you want for your estimate. Let's assume a 95% confidence level.

3. Determine the estimated proportion: If an estimated proportion is provided, use that. Otherwise, assume a proportion based on previous knowledge or conduct a pilot study to estimate the proportion.

4. Find the critical value: Identify the critical value associated with the chosen confidence level. For a 95% confidence level, the critical value is approximately 1.96.

5. Calculate the sample size: Use the formula for calculating the sample size for estimating a proportion:

n = (Z^2 * p * (1 - p)) / E^2

Where:
- n is the required sample size
- Z is the critical value
- p is the estimated proportion
- E is the desired margin of error

Insert the values into the formula and calculate the sample size.

Remember that these calculations are based on certain assumptions, including a random and representative sample. Adjustments may need to be made based on the specific context of the data set or study.