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).
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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