Answered: Vineyard Pines sells clothing online.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Vineyard Pines sells clothing online. In 2020, the mean value of orders placed with the company was $34.50. The President of the company made increasing the amount of the average order a priority for 2021. The company has just received the sales data for 2021. You just received the EXCEL file with details of the 400 orders in in the first quarter of 2021. You began by calculating the univariate statistics. Here are your findings:Total sales revenue:$14,000Number of orders in 2021:400Average order: $35.00Standard deviation of the individual orders: $5.20

Required: Determine the P-Value associated with the change in the average order total in 2021. Note that the company’s strategies for growth could have led to a reduction so we cannot assume a one-directional hypothesis. Given the number of data points (orders), you can assume a normal distribution and therefore assume a z-distribution for the data.

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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