Question

An economist with the Liquor, Hospitality and Miscellaneous Workers' Union collected data on the weekly salaries of workers in the hospitality industry in Cairns and Townsville. The union believed that the weekly salaries of employees in Cairns were higher and they were mounting a case for the equalisation of salaries between the two cities. The researcher took samples of size 32 and 25 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $592.75 and $38.41 respectively in Townsville, and $608.17 and $32.90 in Cairns. Use Cairns minus Townsville.

1. Determine a point estimate for the value of the difference in average weekly salary between the two groups (in dollars to 2 decimal places). Blank 1

2. Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance (in dollars to 2 decimal places). Blank 2

3. Use Kaddstat to determine a 95% confidence interval for the difference between the average weekly salaries in Cairns and Townsville. lower limit Blank 3
upper limit Blank 4 (in dollars to 2 decimal places)

Answer 1

Solution:

Given:

The researcher took samples of size 32 and 25 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $592.75 and $38.41 respectively in Townsville, and $608.17 and $32.90 in Cairns.

That is:

Cairns :

Sample Size = n₁ = 32

Sample Mean =

Sample Standard Deviation = s₁ = 32.90

Townsville:

Sample Size = n₂ = 25

Sample Mean =

Sample Standard Deviation = s₂ = 38.41

We have use Cairns minus Townsville.

Part 1)

Determine a point estimate for the value of the difference in average weekly salary between the two groups.

A point estimate for the value of the difference in average weekly salary between the two groups is given by:

Part 2)

Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance.

Where

Thus

Thus  the standard error for the difference between the means is $ 9.45

Part 3)

Use Kaddstat to determine a 95% confidence interval for the difference between the average weekly salaries in Cairns and Townsville.

Use following steps in Excel  Kaddstat:

( Note: If kaddstat is not installed then download it, then open Excel file,

click on Files -> Options -> Add-inns -> Go -> Browse -> Go to folder where Kaddstat file is saved and select file

then click on Ok,

Close Excel and open it again.)

Click on Add-inns

Select Kaddstat

Confidence Interval

Two Sample

Independent Samples

Enter numbers

Click inside Cell and select any one blank cell for output.

Click on OK

Thus we get

Confidence Interval for
Two Independent Samples
(Equal Variances)
Lower limit =	-3.5220
Upper Limit =	34.3620
Margin for Error (Half Width) =	18.9420
	Sample 1	Sample 2
Mean =	608.1700	592.7500
Standard Deviation =	32.9000	38.4100
Sample Size =	32	25
% Confidence Interval =	0.95

Thus

Lower Limit = -3.52

Upper Limit =34.36