Question

Question 2: Single proportion

A large corporation’s training and development manager wants to determine a 98% confidence interval for the proportion of employees who have enrolled with universities while being employed. A sample of 990 employees indicates that 198 of them have started programmes with universities.

Due to a recent change in its training and development policy, the corporation is required to show that at least 25% of its employees have enrolled with universities while being employed.

Answer the following questions:

• What proportion of the sample employees have enrolled at a university while being employed?
• Navigate to the “Confidence interval” tab and, using the calculated proportion, determine the endpoints of the confidence interval as a proportion of employees. What do these values mean?
• Navigate to the “Sample size” tab and calculate how many more employees should be sampled to estimate the true proportion to within 0.02 (or 2%).
• Based on your calculations of the confidence interval, has the corporation met the requirements of the recent change in its training and development policy?

Answer 1

the proportion of the sample employees have enrolled at a university while being employed =

Q) how many more employees should be sampled to estimate the true proportion to within 0.02

The margin of error:

for 98% confidence

since the population proportion estimate is not given we assume p = 0.5

sample size of 3382 is required

3392 -990 = 2402 more sample is required.

the corporation is required to show that at least 25% of its employees have enrolled with universities while being employed, and 0.25 is outside the limits of the confidence interval calculated above. Thus the corporation didn't met the requirements of the recent change in its training and development policy.