Courier 2 was used 15 times, and their average delivery time was 36 minutes with a standard deviation of 8 minutes. Construct a 95% confidence interval for the difference in the true mean delivery times for Courier 1 and Courier 2 (rounded off to two decimals)
A law firm is evaluating the delivery time of two courier delivery services in Cape Town. They believe that there is a difference between the average delivery times for the two courier services. To investigate this matter further, the firm decides to use both courier services daily over a two month period for deliveries to similar destinations. The delivery times for each courier service are recorded over the two month period. It is found that Courier 1 was used by the firm 12 times and their average delivery time was 43 minutes with of standard deviation of 12 minutes. Courier 2 was used 15 times, and their average delivery time was 36 minutes with a standard deviation of 8 minutes. Construct a 95% confidence interval for the difference in the true mean delivery times for Courier 1 and Courier 2 (rounded off to two decimals).
It is given that
For Courier 1:
Mean, X̅1 = 43
Standard deviation, s1 = 12
Sample size, n1 = 12
For Courier 2:
Mean, X̅2 = 36
Standard deviation, s2 = 8
Sample size, n2 = 15
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