A sociologist claims that the age distribution for the residents of a city is different from the distribution 10 years ago. The distribution of ages 10 years ago is shown in the table at the left. You randomly select 400 residents and record the age of each. The survey results are shown below in the table. At α = 0.05, perform a chi-square goodness-of-fit test to test whether the distribution has changed.

a. Verify that the expected frequency is at least 5 for each category.

b. Identify the expected distribution and state H0 and Ha.

c. Identify the level of significance α.

d. Identify the degrees of freedom.

e. Find the critical value X₀² and identify the rejection region.

f. Find the chi-square test statistic. Sketch a graph.

g. Decide whether to reject the null hypothesis.

h. Interpret the decision in the context of the original claim.

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Previous age Survey results Ages 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70+ distribution 16% 20% 8% 14% 15% 12% 10% 590 76 84. 30 60 54 40 42 14