According to data only 32% of Americans are saving for retirement in a 401(k). A random sample of 340 Americans was recently selected, and it was found that 118 of them made contributions to their 401(k) plans this year. a. Using α = 0.01, conduct a hypothesis test to determine if the percentage of Americans who have made contributions to their 401(k) plans this year is more than 32%. Be sure to clearly state your conclusions. b. Perform the same hypothesis test two more times, using α = 0.05 and α = 0.10, respectively. Have your conclusions changed based on either of these two new tests? c. How would the hypothesis test have been different if all you wanted to determine was that the percentage of Americans who have made contributions to their 401(k) plans this year is different from 32%? Perform this test at the α = 0.05 significance level and state your conclusions.
According to data only 32% of Americans are saving for retirement in a
401(k). A random sample of 340 Americans was recently selected, and it was found that 118 of them made contributions to their 401(k) plans this year.
a. Using α = 0.01, conduct a hypothesis test to determine if the percentage of Americans who have made contributions to their 401(k) plans this year is more than 32%. Be sure to clearly state your conclusions.
b. Perform the same hypothesis test two more times, using α = 0.05 and α = 0.10, respectively. Have your conclusions changed based on either of these two new tests?
c. How would the hypothesis test have been different if all you wanted to determine was that the percentage of Americans who have made contributions to their 401(k) plans this year is different from 32%? Perform this test at the α = 0.05 significance level and state your conclusions.
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