Question

A tax policy thinktank sent out a report stating that less than 70% of all Fortune 500 firms paid any corporate income tax. We don’t believe them, so we plan to take a sample of 50 firms and investigate to see what proportion of them paid corporate income taxes

a. Are we doing this hypothesis test to support our research, challenge a claim, or take an action?

b. State Ho and Ha.

c. What does it mean for this problem if we reject Ho?

d. What does a Type I error mean for this specific problem?

Answer 1

a. Purpose of the hypothesis testing is to check whether we have sufficient evidence to support the claim

Hence answer here is we are doing this hypothesis test to challenge a claim.

b. Here it is given that A tax policy thinktank sent out a report stating that less than 70% of all Fortune 500 firms paid any corporate income tax.

As we know null hypothesis always have equality sign

So hypothesis is vs

c. If we reject H0, which means we have sufficient evidence to suppor the claim that p<0.7

d. As we know In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis.

Hence here Type 1 error means p is not less than 0.7, infact it is equal to 0.7 but we conclude it to be less than 0.7