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 sample proportion is 112/150, about 0.747, and the advisor is testing whether the true proportion is below 0.80. To make a test more likely to detect a real difference from 0.80, the advisor can increase its power by using a larger sample and a larger significance level. A larger significance level makes it easier to reject the null hypothesis, though it also increases the chance of a Type I error. Thus, the choice describing a sample larger than 150 and α larger than 0.05 is correct.

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