Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations. Row 1 Row 2 Row 3 Total i i Row 1 i Row 2 i Row 3 42 a. Write the null and alternative hypotheses for a test of homogeneity for this table. Ho: The proportion in each row is ✓for all four populations. i Sample Selected From Population 1 i 42 i 13 i 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. Population 1 Population 2 Population 3 Population 4 81 Population 2 57 42 i i 110 i 80 i 68 55 Population 3 123 103 Population 4 i i i i i i i i Total

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c. For α = 0.025, find the critical value of x². Specify the rejection and nonrejection regions on the chi-square distribution curve.
Enter the exact answer from the chi-square distribution table.
x²
=
The rejection region is
of the critical value of x².
The nonrejection region is
d. Find the value of the test statistic x².
Round your answer to three decimal places.
The value of the test statistic x² is i
e. Using a = 0.025, would you reject the null hypothesis?
V
of the critical value of x².
Transcribed Image Text:c. For α = 0.025, find the critical value of x². Specify the rejection and nonrejection regions on the chi-square distribution curve. Enter the exact answer from the chi-square distribution table. x² = The rejection region is of the critical value of x². The nonrejection region is d. Find the value of the test statistic x². Round your answer to three decimal places. The value of the test statistic x² is i e. Using a = 0.025, would you reject the null hypothesis? V of the critical value of x².
Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four
populations.
Row
1
Row
2
Row
3
Total
Row 1
IN
Row 2
i
Sample Selected From
Population 1 Population 2 Population 3 Population 4
42
13
Row 3 42
a. Write the null and alternative hypotheses for a test of homogeneity for this table.
Ho: The proportion in each row is
for all four populations.
81
57
Population 2
42
110
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.
Population 1
80
68
55
Population 3
123
103
Population 4
Total
Transcribed Image Text:Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations. Row 1 Row 2 Row 3 Total Row 1 IN Row 2 i Sample Selected From Population 1 Population 2 Population 3 Population 4 42 13 Row 3 42 a. Write the null and alternative hypotheses for a test of homogeneity for this table. Ho: The proportion in each row is for all four populations. 81 57 Population 2 42 110 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. Population 1 80 68 55 Population 3 123 103 Population 4 Total
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