random sample of 9600 students. Multistage design effect similar to an SRS (for those still in school)
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 students 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 will use the given information about the random sample of 9600 students.
To get the estimate with 99% confidence, we can use the formula for margin of error:
Margin of Error = Z * sqrt((p * (1-p))/n)
Where:
- Z is the z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a z-score of approximately 2.58).
- p is the proportion of the sample that has the desired characteristic (46% or 0.46 in decimal form).
- n is the sample size (9600 students).
Using the formula, we can calculate the margin of error:
Margin of Error = 2.58 * sqrt((0.46 * (1-0.46))/9600)
The margin of error gives us a range within which the true population proportion is likely to fall. To obtain the estimated proportion, we subtract the margin of error from the sample proportion and add it to the sample proportion:
Estimated Proportion = Sample Proportion ± Margin of Error
Estimated Proportion = 0.46 ± (2.58 * sqrt((0.46 * (1-0.46))/9600))
Now, regarding the question of whether the proportion of all students with at least one parent who was a college graduate would be higher or lower than 46%:
Since the sample does not include dropouts, it is likely that the proportion of all students with at least one parent who was a college graduate would be higher than 46%. This is because dropouts may be less likely to have parents who are college graduates. By excluding them from the sample, the overall proportion of students with college graduate parents is likely to be higher than the proportion observed in the sample.
However, it's important to note that this is an inference based on the available information and assumes that the multistage design effect has minimized biases. Further research and analysis would be necessary to determine the true proportion with more certainty.