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 northern cities. The researcher took samples of size 30 and 37 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $585.43 and $38.72 respectively in Townsville, and $616.19 and $29.13 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).

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).   

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

Answer 1

(1) point estimate for the value of the difference in average weekly salary between the two groups=616.19-585.43= $30.76.

(2)

(3) 5% confidence interval for the difference between the average weekly salaries in Cairns and Townsville:

Lower limit=$13.70

Upper limit=$47.82