Question

You would like to "prove" your alternative hypothesis that the proportion of all male college students who can run a mile in less than 7.5 minutes is less than 0.30. You collect a random sample of college males and discover that 26.0% of them can run a mile in less than 7.5 minutes. Let n be the sample size. Which of the following can you conclude?

a. If n= 250, then these results are significant at the 5% level, but not at the 1% level.

b. If n= 1000, then these results are significant at the 5% level, but not at the 1% level.

c. If n= 500, then these results are significant at the 5% level, but not at the 1% level.

d. If n=100, then these results are significant at the 10% level, but not at the 5% level.

Answer 1

sample success x   =		130
sample size          n    =		500
std error   se =√(p*(1-p)/n) =		0.0205
sample proportion p̂ = x/n=		0.2600
test stat z =(p̂-p)/√(p(1-p)/n)=		-1.95
p value                          =		0.0256

since p value is between 0.05 and 0.01

option C is correct

c. If n= 500, then these results are significant at the 5% level, but not at the 1% level.