A random sample of 150 employees was selected. There are 60 employees older than 30 in the sample. Estimate the proportion of all employees of the company who are older than 30 with a 50% confidence.
A) We can be 50% confident that the true proportion of all employees of the company who are older than 30 is 0.4.
B) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.334, 0.466).
C) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.322, 0.478).
D) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.38, 0.42).
E) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.36, 0.44).

Question

A random sample of 150 employees was selected. There are 60 employees older than 30 in the sample. Estimate the proportion of all employees of the company who are older than 30 with a 50% confidence. ​
A) We can be 50% confident that the true proportion of all employees of the company who are older than 30 is 0.4.
B) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.334, 0.466).
C) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.322, 0.478).
D) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.38, 0.42).
E) We can be 50% confident that the true proportion of all employees of the company who are older than 30 falls within the interval (0.36, 0.44).

Quizplus · Accepted Answer

The proportion of employees older than 30 in the sample is 60/150 = 0.4, or 40%. A 50% confidence interval estimate would require more information (like standard deviation or standard error) to calculate an interval. However, without that information and based on the choices provided, stating the sample proportion (0.4) as the estimate for the true proportion is the most straightforward answer.

A Random Sample of 150 Employees Was Selected