AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Testing a Claim about a Population ProportionQuestion 8
8
QuizMultiple Choice

Testing a Claim about a Population Proportion

Question 8 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

An emergency fund is defined as a savings account that has a balance equal to at least two months’ living expenses. An article in a financial magazine claims that 80% of American adults do not have an emergency fund. To investigate this claim, a financial advisor selects a random sample of 150 American adults and finds that 112 do not have an emergency fund. The financial advisor would like to know if the data provide convincing evidence that the true proportion of Americans who do not have an emergency fund is less than 80%. What are the appropriate hypotheses for this test?

Answer
A
H0: p = 0.80 versus Ha: p < 0.80, where p = the true proportion of all American adults who do not have an emergency fund.
B
H0: p < 0.80 versus Ha: p = 0.80, where p = the true proportion of all American adults who do not have an emergency fund.
C
H0: p = 0.80 versus Ha: p < 0.80, where p = the proportion of American adults in the sample who do not have an emergency fund.
D
H0: p < 0.80 versus Ha: p = 0.80, where p = the proportion of American adults in the sample who do not have an emergency fund.

Explanation

The claim is about the true proportion of all American adults who do not have an emergency fund, so p must represent that population proportion—not the sample proportion. Because the advisor is testing whether the true proportion is less than 0.80, the alternative hypothesis is Ha: p < 0.80. The null hypothesis uses the claimed value, H0: p = 0.80. Thus, the correct choice is “H0: p = 0.80 versus Ha: p < 0.80,” with p defined as the true proportion of all American adults who do not have an emergency fund.

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