Preparing to Conduct a Chi-Square Test for Goodness of Fit — Quiz
Question 5 • Statistics
According to a government website, 42 percent of US citizens are Democrats, 34 percent are Republicans, and 24 percent are Independents. A local municipality would like to know if the distribution of political party affiliation among its citizens differs from the nationwide percentages. A random sample of 500 citizens of the municipality is selected. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : The distribution of political party in the municipality is 42 percent Democrat, 34 percent Republican, and 24 percent Independent. cap h sub A : The distribution of political party in the municipality is not 42 percent Democrat, 34 percent Republican, and 24 percent Independent.
B
cap h sub 0 : The sample will not contain 210 Democrats, 170 Republicans, and 120 Independents. cap h sub A : The sample will contain 210 Democrats, 170 Republicans, and 120 Independents.
C
cap h sub 0 : The sample will contain 210 Democrats, 170 Republicans, and 120 Independents. cap h sub A : The sample will not contain 210 Democrats, 170 Republicans, and 120 Independents.
D
cap h sub 0 : The distribution of political party in the municipality is not 42 percent Democrat, 34 percent Republican, and 24 percent Independent. cap h sub A : The distribution of political party in the municipality is 42 percent Democrat, 34 percent Republican, and 24 percent Independent.
Explanation
The question asks whether the municipality’s population distribution differs from the nationwide percentages. The null hypothesis states that the municipality has the nationwide distribution: 42% Democrat, 34% Republican, and 24% Independent. The alternative states that its distribution is different, so choice A is correct. Hypotheses describe population proportions, not the exact counts in one sample.
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