Chapter 11, Section 11.3, Problem 022 Consider the following contingency table t

ID: 3311653 • Letter: C

Question

Chapter 11, Section 11.3, Problem 022

Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations.

a. Write the null and alternative hypotheses for a test of homogeneity for this table.

H0: The proportion in each row is

for all four populations.

H1: The proportion in each row is

for all four populations.

b. Calculate the expected frequencies for all cells assuming that the null hypothesis is true.

Round your answers to three decimal places, where required.

c. For =0.025, find the critical value of 2. Specify the rejection and nonrejection regions on the chi-square distribution curve.

Enter the exact answer from the chi-square distribution table.

The rejection region is

of the critical value of 2. __________

d. Find the value of the test statistic 2.

Round your answer to three decimal places.

The value of the test statistic 2 is : ________

e. Using =0.025, would you reject the null hypothesis?

Sample Selected From Population 1 Population 2 Population 3 Population 4 Row 1 41 76 117 49 Row 2 18 58 81 113 Row 3 35 46 61 113

Using Minitab:

Chi-Square Test: Population 1, Population 2, Population 3, Population 4

Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts

Population 1 Population 2 Population 3 Population 4 Total
1 41 76 117 49 283
32.92 63.04 90.71 96.32
1.981 2.662 7.617 23.246

2 18 58 81 113 270
31.41 60.15 86.55 91.89
5.726 0.077 0.356 4.848

3 35 46 61 113 255
29.67 56.81 81.74 86.79
0.959 2.056 5.262 7.916

Total 94 180 259 275 808

Chi-Sq = 62.705, DF = 6, P-Value = 0.000

c.Critica chi sqyare value is 14.44 ............use excel function =CHIINV(0.025,6)

d.Test statisstic value is 62.0705

e. Yes. Here p-value 0.000< alpha=0.025 so we reject null hypothesis.

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