random sample of 9600 students.

46% had at least one parent who was a college graduate.
Estimate with 99% confidence the proportion of all students who had at least one parent who was a college grad.

b) Sample does not include drop outs so estimate is valid only for students.
Do you think proportion of ALL those with at least one parent who was college grad would be higher of lower than 46%. Explain

Thank you

To estimate the proportion of all students who had at least one parent who was a college graduate, we need to use the concept of confidence intervals. In this case, since we have a random sample of 9600 students, we can apply the formula for confidence intervals for a proportion.

Step 1: Calculate the standard error
The standard error can be found using the formula:
SE = sqrt[(p̂ * (1 - p̂)) / n]
where p̂ is the proportion in the sample (46% = 0.46) and n is the sample size (9600).

SE = sqrt[(0.46 * (1 - 0.46)) / 9600]
SE = sqrt(0.0015456)
SE ≈ 0.0393

Step 2: Determine the critical value
The critical value depends on the desired level of confidence. Since we want a 99% confidence interval, we need to find the z-value associated with a 99% confidence level. For a large sample size, like in this case, the critical z-value for a 99% confidence level is approximately 2.58.

Step 3: Calculate the margin of error
The margin of error is found by multiplying the standard error by the critical value:
Margin of Error = z * SE
Margin of Error = 2.58 * 0.0393
Margin of Error ≈ 0.101394

Step 4: Calculate the confidence interval
The confidence interval is calculated by subtracting and adding the margin of error to the sample proportion:
Confidence Interval = p̂ ± Margin of Error
Confidence Interval = 0.46 ± 0.101394
Confidence Interval = (0.3586, 0.5614)

Therefore, we estimate with 99% confidence that the proportion of all students who had at least one parent who was a college graduate falls in the range of 0.3586 to 0.5614.

As for whether the proportion of ALL those with at least one parent who was a college graduate would be higher or lower than 46%, it is difficult to say without knowing the characteristics of the entire population. However, since this estimate is derived from a random sample, there is a chance that the true proportion in the population is different from 46%. We can be 99% confident that the true proportion falls within the given confidence interval, but it is not guaranteed to be exactly 46%.