Answered: Define μ as the population mean…

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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When considering the future performance of a company, financial analysts often use forecasts for earnings per share (EPS). Naturally, we are interested in the quality of these forecasts. We can define a forecasting error as follows:

Forecasting Error = Predicted Value of the Variable – The Actual Value of the Variable.

The optimal forecast would have a mean forecasting error of zero. This suggests that, on average, the predicted value is equal to the actual value. Therefore, we construct a hypothesis test to see if the mean forecasting error is equal to zero. You have collected data, as shown in the picture below, for two analysts covering different industries. Analyst A covers the pharmaceutical sector; Analyst B covers the retail sector.

Please complete the following tasks (1–3) and provide an answer to the following question (4):

Define μ as the population mean forecasting error and formulate the null and alternative hypothesis for a zero mean test of forecasting quality.
For Analyst A, use both a t-test and a z-test to determine whether to reject the null hypothesis at the 0.05 and 0.01 levels of significance.
For Analyst B, use both a t-test and a z-test to determine whether to reject the null at the 0.05 and 0.01 levels of significance.
What conclusions do you reach about the forecasts for Analyst A and the forecasts for Analyst B?

Financial Analyst A
Financial Analyst B
Number of Forecasts
201
121
Mean Forecast Error
(Predicted - Actual)
0.06
0.01
Standard Deviations of
Forecast Errors
0.12
0.11

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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