One cable company claims that it has excellent customer service. In fact, the company advertises that a technician will arrive within 55 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming that it takes over 55 minutes for the cable technician to arrive. The customer asks a simple random sample of 4 other cable customers how long it has taken for the cable technician to arrive when they have called for one. The sample mean for this group is 62.1 minutes with a standard deviation of 8.3 minutes. Assume that the population distribution is approximately normal. Test the customer’s claim at the 0.05 level of significance.   Step 3 of 3: Draw a conclusion and interpret the decision.   1. We reject the null hypothesis and conclude that there is suffiecient evidence at a 0.05 level of significance to support the belief that it takes over 55 minutes for the cable technacian to arrive.   2. We reject the null hypothesis and conclude that there is insuffiecient evidence at a 0.05 level of significance to support the belief that it takes over 55 minutes for the cable technacian to arrive.   3. We fail to reject he null hypothesis and conclude that there is insuffiecient evidence at a 0.05 level of significance to support the belief that it takes over 55 minutes for the cable technacian to arrive.   4. We fail to reject he null hypothesis and conclude that there is suffiecient evidence at a 0.05 level of significance to support the belief that it takes over 55 minutes for the cable technacian to arrive.

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 + ...