Question

A dean of a business school wanted to know whether the graduates of her school used the statistic skills that they learn in university during their first year of employment after graduation. As of today there are 34,050 graduates in total from the business school.   The Dean is committed to allocate more funding to the development of the school’s statistics course if at least 17% of its graduates use statistics skills during their first year of employment. She surveyed 500 graduates. 105 graduates responded that they actually find the statistic skills they learnt in university useful and applicable in their first year of employment. Estimate with 95% confidence the proportion of all of the business school graduates who use their statistic skills during their first year of employment.      

1. You were recently hired as a data analyst working for the business school. Specify the appropriate formula you would use to solve the problem. Provide a brief reason why you chose the formula.    

2. Obtain the 95% confidence interval estimate of the proportion of all of the business school graduates who use their statistic skills during their first year of employment.      

                Display working.

3. Provide an interpretation of the answers you obtained in part b) in the context of the problem.   
4. Based on the interval estimation you just conducted, present brief statements of two or three sentences to the Dean. Should she allocate more funding for the

                development of the statistics course? Yes or no? Why?

5. Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when a lower sample size is used?                                                                             

Answer 1

(a)

The appropriate formula we would use to solve the problem. :

where

= Sample Proportion

= Critical value of Z for significance level

n = Sample Size

Reason:

This test satisfies all thconditions of a one - sample proportion Z test as follows:

(i) The data are a Simple Random Sample (SRS) from the population of interest

(ii) The population (N = 34,050) is at least 10 times as large as the sample (n = 500)

(iii)

np = 500 X 0.17 = 85 10

n (1 - p) = 500 X 0.83 = 415 10

So,

all conditions are satisfied.

(b)

(i)

Confidence Interval:

Answer is:

(0.174, 0.246)

(ii)

Interpretation:

The 95% Confidence Interval (0.174, 0.246) is a range of values we are 95% confident will contain the true unknown population proportion of all of the business school graduates who use their statistic skills during their first year of employment.

(iii) Since all values in the confidence interval (0.174, 0.246) are greater than 0.17, the Dean should allocate more funding for the development of the statistics course.

So,

Correct option:

Yes

Reason:

All values in the confidence interval (0.174, 0.246) are greater than 0.17

(iv)

The width of the interval increases when a lower sample size is used