Question 6 • 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 Americans 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 American adults who do not have an emergency fund is less than 80%. The financial advisor tests the hypotheses H0: p = 0.80 versus Ha: p < 0.80, where p = the true proportion of all American adults that do not have an emergency fund. The conditions for inference are met. The standardized test statistic is z = –1.62 and the P-value is 0.0526. What conclusion should the financial advisor make using the α = 0.05 significance level?
Answer
A
Because the P-value is greater than α = 0.05, there is convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%.
B
Because the P-value is greater than α = 0.05, there is convincing evidence that the true proportion of American adults who do not have an emergency fund is greater than 80%.
C
Because the P-value is greater than α = 0.05, there is not convincing evidence that the true proportion of American adults who do not have an emergency fund is less than 80%.
D
Because the P-value is greater than α = 0.05, there is not convincing evidence that the true proportion of American adults who do not have an emergency fund is greater than 80%.