Question

Chi-Square Test of Goodness of Fit. FOR THIS AND THE NEXT PART. The historical market shares of 4 firms are shown below. Also shown is the number of customers who, in a recent survey, indicated which firm they patronize. Note that the total number of customers in the survey is 200.

Firm	Historical Market Share	Number of Recent Customers in Survey
1	0.40	70
2	0.32	60
3	0.24	54
4	0.04	16

2.       In order to test whether the market shares have changed - in light the recent survey results - the following null hypothesis is defined for each firm:

3.       H₀: p1 = 0.40, p2 = 0.32, p3 = 0.24, p4 = 0.04

4.       Calculate the chi-square statistic for this study. Note: to do this, you should first calculate the "expected number" of customers for each firm based on the historical market share and the surveyed number of 200 customers.

		7.81
		10.25
		12.55
		None of the above

  

PART 2

1.       Chi-Square Test of Goodness of Fit. CONTINUING FROM THE PRECEDING. What is the critical value of the test statistic? What can we conclude from the result?

		Critical value = 7.81. At least one of the market shares differs from its historical value
		Critical value = 10.25. At least one of the market shares differs from its historical value
		Critical value = 12.55. The market shares have not changed significantly from their historical levels
		None of the above of completely correct

Answer 1

Answer:

4.       Calculate the chi-square statistic for this study. Note: to do this, you should first calculate the "expected number" of customers for each firm based on the historical market share and the surveyed number of 200 customers.

The correct answer is

Explanation:

The test statistic is:

Part 2

1.       Chi-Square Test of Goodness of Fit. CONTINUING FROM THE PRECEDING. What is the critical value of the test statistic? What can we conclude from the result?

Answer: Critical value = 7.81. At least one of the market shares differs from its historical value

Explanation:

The chi-square critical value at 0.05 significance level for df = n - 1 = 4 - 1 = 3. Using the chi-square table, we have:

Since the chi-square test statistic is greater than the chi-square critical value, we , therefore, reject the null hypothesis and conclude that at least one of the market shares differs from its historical value.