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?
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%.
A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. What are the appropriate hypotheses for this test?
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?
It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. Are the conditions for inference met for conducting a z-test for one proportion?
According to a soccer coach, 75% of soccer players have had at least one sprained ankle. An athletic trainer would like to investigate this claim. To do so, the trainer selects a random sample of 125 college soccer players from across the country and finds that 99 of them have had at least one sprained ankle. The trainer would like to know if the data provide convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. The computer output gives the results of a z-test for one proportion.Test and CI for One ProportionTest of p = 0.75 vs p > 0.75Sample1X99N125Sample p0.79295% CI(0.72085, 0.86315)Z-Value1.084P-value0.1391
According to a soccer coach, 75% of soccer players have had at least one sprained ankle. An athletic trainer would like to investigate this claim. To do so, the trainer selects a random sample of 125 college soccer players from across the country and finds that 99 of them have had at least one sprained ankle. The trainer would like to know if the data provide convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. What are the appropriate hypotheses for this test?
According to a soccer coach, 75% of soccer players have had at least one sprained ankle. An athletic trainer would like to investigate this claim. To do so, the trainer selects a random sample of 125 college soccer players from across the country and finds that 99 of them have had at least one sprained ankle. The trainer would like to know if the data provide convincing evidence that the true proportion of college soccer players who have had at least one sprained ankle is greater than 75%. The computer output gives the results of a z-test for one proportion.Test and CI for One ProportionTest of p = 0.75 vs p > 0.75Sample1X99N125Sample p0.79295% CI(0.72085, 0.86315)Z-Value1.084P-value0.1391
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 conditions for inference are met. What is the value of the test statistic and P-value for this test?
Did you find these answers helpful?