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6. (6 marks) (Do this question by hand, showing all your working clearly and stating all used formulas) Over the past year aggressive construction of residential homes has occurred in the Kitchener-Waterloo region. With the success experienced in the region, one of the large construction companies would like to expand its operations into a new geographical area. They have narrowed their choice to one of two cities. To make a more informed decision they want to investigate the average hourly wage they must pay for general laborers. The company randomly selects labourers from each city and determines their hourly wage. The data is summarised in the table below. n X S City A 20 $15 $3 City B 35 $16 $2 a) (4) Assuming that the population variances are approximately equal, calculate a 99% confidence interval for the difference in average hourly wage between City A and City B. b) (2) Based on your confidence interval, does there appear to be a significant difference in the average hourly wage between City A and City B? Explain your conclusion and indicate the significance level being used