A marketing researcher wants to estimate the mean savings ($) realized by shoppers who showroom. Showrooming is the practice of inspecting products in retail stores and then purchasing the products online at a lower price. A random sample of 100 shoppers who recently purchased a consumer electronics item on-line after making a visit to a retail store yielded a mean savings of $ 58 and a standard deviation of $ 55. a. construct a 95% confidence interval estimate for the mean savings for all showroomers who purchased a consumer electronics item. b. Suppose the owners of a consumer electronics retailer wants to estimate the total value of lost sales attributed to the next 1000 showroomers that enter their retail store. How are the results in (a) useful in assisting the consumer electronics retailer in their estimation

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 + ...