Consider the following contingency table that records theresults obtained for four samples of fixed sizes selected from fourpopulations.
| Sample Selected From |
|---|
| Population 1 | Population 2 | Population 3 | Population 4 |
|---|
| Row 1 | 38 | 75 | 90 | 79 |
| Row 2 | 16 | 56 | 82 | 123 |
| Row 3 | 45 | 49 | 78 | 78 |
a. Write the null and alternative hypothesesfor a test of homogeneity for this table.
H0: The proportion in each row is
the same/not the same
for all four populations.
H1: The proportion in each row is
not the same/the same
for all four populations.
b. Calculate the expected frequencies for allcells assuming that the null hypothesis is true.
Round your answers to three decimal places, where required.
| Population 1 | Population 2 | Population 3 | Population 4 | Total |
| Row 1 | | | | | |
| Row 2 | | | | | |
| Row 3 | | | | | |
| Total | | | | | |
c. For α=0.025, find the critical value of χ2.Specify the rejection and nonrejection regions on the chi-squaredistribution curve.
Enter the exact answer from the chi-square distributiontable.
χ2=
The rejection region is
on the right/on the left
of the critical value of χ2.
The nonrejection region is
on the right/on the left
of the critical value of χ2.
d. Find the value of the test statistic χ2.
Round your answer to three decimal places.
The value of the test statistic χ2 is .
e. Using α=0.025, would you reject the nullhypothesis?
No./Yes.
