Question

Suppose a recent business article reported that 25% of small business owners in the United States preferred a Simplified Employee Pensions Individual Retirement Account (SEP IRA) to a Roth IRA. The local chamber of commerce wanted to see if the proportion of small business owners who prefer the SEP IRA was greater in their community. They randomly sampled 100 small business owners and asked which of the two retirement accounts they preferred.

The survey found that 32 small business owners preferred the SEP IRA. A one-sample z‑test will be used to determine if the local community proportion is greater than the proportion in the United States. Choose the claim that best completes the following sentence.

The proportion of small business owners in the:

a) United States who favor the SEP IRA is greater than 32%.

b) United States who favor the SEP IRA is less than 32%.

c) local community who favor the SEP IRA is greater than 32%.

d) United States who favor the SEP IRA is equal to 25%.

e) local community who favor the SEP IRA is greater than 25%.

f) local community who favor the SEP IRA is equal to 32%.

Answer 1

At a 5% significance level, critical t=1.645 and at 10% significance level, critical t=1.28

Hence, at 5% significance level, we can say the small business owners in the US who favor SEP IRA is equal to 0.25.

However, at 10% significance level, we can say the small business owners in the US who favor SEP IRA is greater than 0.25.

So, the answer would depend on the significance level assumed. But, overall I would prefer the answer as greater than 0.25 as the critical t at 5% is close to the test statistic.