# Chi square goodness of fit test, ANOVA

1) A sales manager is curious whether day of the week makes any difference in number of sales made. She decides to sample the records to determine if sales are distributed evenly throughout the six-day workweek. The sample results are:

Day of Week Sales Made

Monday 6

Tuesday 9

Wednesday 11

Thursday 10

Friday 10

Saturday 18

Total 64

a. What are the hypotheses for your research design?

b. What is the critical value for the X^2 statistic at a .05 level of significance? State your decision rule.

c. Compute the X^2 for this goodness of fit test.

d. On the basis of your results, are there significant differences between days? Explain the rationale for your results with a short summary statement of your research and at least one recommendation for the sales manager.

2) The sales manager is pleased with the results of your initial research study and give you another challenge. She asks you to study the results of three sales approaches to see if one of the approaches would result in increased sales. The approaches are:

1. a sales-information DVD mailed to prospective customers

2. a personal sales call

3. a telephone call to prospective customers

A random sample of 340 recent customers were selected. The results, in terms of purchases of the full program tapes are as follows:

Observed Sales Approach

Action DVD Personal sales call Telephone call Total

Purchased 17 35 20 72

Return 81 84 103 268

Total 98 119 123 340

Expected Sales Approach

Action DVD Personal sales call Telephone call Total

Purchased

Return

Total

e. What are the hypotheses for your research design?

f. Compute the expected frequencies for each cell in the second table.

g. What is the table value for the X^2 statistic at a .01 level of significance? State your decision rule.

h. Compute the X^2 for this contingency table.

i. What are the hypotheses for your research design?

j. On the basis of your results, what is your decision? Explain the rationale for your results with a short summary statement of your research and at least one recommendation for the sales manager.

3. After running a regression to determine a predictive model for sales (monthly revenue in thousands) based on average number of hours spent per day making sales calls by your sales staff, you come up with the following regression output:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.92

R Square 0.84

Adjusted R Square 0.81

Standard Error 89.59

Observations 7.00

ANOVA

df SS MS F

Regression 206907.64

Residual

Total 247041.43

Coefficients Standard Error t Stat

Intercept 136.33 71.89 1.90

Sales persons 70.43 13.87 5.08

1. Complete the ANOVA table. What is the computed F statistic? How many degrees of freedom are there in this regression? Is the model significant?

2. How much variation in the data is explained? How much is left unexplained?

3. If salespersons spend 6 hours per day making sales calls, how much revenue can the Sales Manager expect to earn this month?

See the attached file and respond to the following:

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1. Complete the ANOVA table. What is the computed F statistic? How many degrees of freedom are there in this regression? Is the model significant?

2. How much variation in the data is explained? How much is left unexplained?

3. If salespersons spend 6 hours per day making sales calls, how much revenue can the Sales Manager expect to earn this month?

#### Solution Summary

Tests hypothesis using Chi square goodness of fit test, ANOVA etc.