Does the data indicate that the revised (one week) forecast is significantly more accurate than the first (one month) forecast? In order to find out whether the revised forecast is significantly more accurate than the first forecast, we can use t-test to

Authors Avatar

Question1

A company supplying parts to a large customer receives forecasts of the expected demand in advance of the delivery date. One forecast is received one month ahead of delivery and a revised forecast is received one week ahead of delivery (i.e. three weeks after the first forecast). Finally, the actual requirements are indicated electronically on the delivery date. The following table shows that the data sent to the supplier covering a period of six months (twenty four weeks).

(i) Does the data indicate that the revised (one week) forecast is significantly more accurate than the first (one month) forecast?

In order to find out whether the revised forecast is significantly more accurate than the first forecast, we can use t-test to test whether the means are equal for two populations.

At first, we calculate the errors of both forecasts, which give us the following data:

In order to test whether the revised forecast is more accurate than the first one, the paired t-test could be used.  

Define the question: is the result from the revised forecast more accurate than that of the first forecast?

Identify the appropriate model: as the mean difference is required and samples are small and not independent, we choose paired t-test.

Difference could be in either way; therefore, it is a two-tailed test.

Formulate the Null hypothesis and the Alternative hypothesis (H0 and H1):

  H0: µ12

H1: µ1≤µ2

The level of significance is α = 5%, then α/2 = 2.5%. With degrees of freedom,ν=23,from Statistical Table, 5, tcrit = 2.069.

tcalc =  = -2.77, with =191.58, =338.59

tcalc > tcrit                  

 Reject H0. In other words, the result of revised forecast is more accurate than that of the first forecast.

(ii) The forecasting method assumes that the errors are normally distributed. Does the data support this assumption for each of the two forecasts?

In this case, the “Goodness of Fit” χ2-test can be applied to testify whether Normal Distribution model is suitable or not.

  1. The errors of the first ( 1 month ahead ) forecast

Define the question: does a Normal distribution model fit the data?

Identify the appropriate model: it is obviously a “Goodness of Fit” question, so χ2-test can be used.

As “fit” can be “too bad” to accept H0, but it is can never be “too good” to accept H0. Therefore, it is a One-tailed test.

Formulate the Null hypothesis and the Alternative hypothesis (H0 and H1):

H0 : Normal distribution model does fit the data

H1: Normal distribution model does not fit the data

The level of significance is set at α=5%.

The data are rearranged by chi-square test of Statpro package.

Table 1. Excel StatPro package- Chi-square test for errors of one month ahead forecast

As displayed in the above table, the frequencies of the first three categories are blow 3. Because the χ2 does not work very well with small frequencies, the categories of <=(-1800), (-1800)-(-1500), and (-1500)-(-1200) are combined to together, which gives the number of cell k=5.

The degrees of freedom ν equal to k-p-1, where k is the number of cells, p is the number of parameters estimated from the sample data of the proposed distribution. In the case of normal distribution, the value of the sample mean and standard deviation are required to calculate the Expected values, therefore, p=2.  ν=5−2−1=2

From Statistical Table 7, with ν=2, χ²crit=5.991

From Table 1. the total distance measures equals to the Chi-square statistics 5.359, which is calculated by the Chi-square test in StatPro package in Excel. The Chi-square test :χ²calc = ∑ (O E) ² ∕ E, which gives us χ²calc= 5.359.

Therefore, χ²calc χ²crit , H0 is accepted. As a result, the normal distribution is an adequate model for the data of errors of first forecast.

Join now!

  1. The errors of second (one week ahead) forecast

Define the question: does a Normal distribution model fit the data?

Identify the appropriate model: it is obviously a “Goodness of Fit” question, so χ2-test can be used.

As “fit” can be “too bad” to accept H0, but it is can never be “too good” to accept H0. Therefore, it is a One-tailed test.

Formulate the Null hypothesis and the Alternative hypothesis (H0 and H1):

H0 : Normal distribution model does fit the data

H1: Normal distribution model does not fit the data

The level ...

This is a preview of the whole essay