Assignment 3
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Business Finance
Description
¹¹¹ Chi –Square Distribution to test
the independence of two variables
Step 1: Set up the hypotheses:
H The software made no difference in sales.
H¹ The software increased sales.
Step 2: Compute the expected frequency for each cell in the contingency table by use of the formula:
E=Expected frequency= (Row total)(Column Total)
_____________________
Sample size
Step 3: Compute the statistic χ ²=Σ(O-E)² / E
Where O is the observed frequency, E is the expected
frequency and the sum Σ are over all cells.
Step 4: Find the critical value χ²α in Table A. 10 page 648. Use the level of significance of 0.01 and the number of degrees of freedom. d.f. to find the critical value.
d.f.= (R-1)(C-1) ( 2-1) (4-1)= 3
Critical Value= 11.3449
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where R is the number of rows and C is the number of columns of cells in the contingency table. The critical region consists of all values of χ²α.
Step5: Compare the sample statistic χ² of Step 3 with the critical value of χ²α of Step 4. If the sample statistic is larger, reject the null hypothesis of independence. Otherwise, do not reject the null hypothesis.
Problem
Company W is testing a sales software. It sales force of 500 people is divided into four regions: Northeast, Southeast, Central and West. Each sales person is expected to sell the same amount of products. During the last 3 months , only half of the sales representatives in each region were given the VP of Sales at WidgeCorp, who is comfortable with
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statistics, wants to know the possible null and alternative hypotheses for a nonparametric test on this data using the chi-square distribution. A nonparametric test is used on data that are qualitative or categorical, such as gender, age group, region and color. It is used when it does not make sense to look at the mean of such variables.
Use the chi-square test to determine if the software increased sales at the 0.01 level of significance.
Sales Sales Sales Sales Row Totals
__NE________SE______C______W_______________________
200 225 200 250 875 Software
115 75 120 80 390 No Software
315 300 320 330 1265
Use the chi square test to determine if the software made a difference in sales at the 0.01 level of significance.
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