Question

Binge Drinking: Binge drinking is defined by the U.S. Department of Health and Human Services as the consumption of 5 or more drinks in a row for men and 4 or more for women. In a recent study of 450 college students, 240 of them reported to have engaged in binge drinking in the past two weeks. The report concluded that half of all college students binge drink. Test this claim at the 0.10 significance level.

(a) What type of test is this?

This is a right-tailed test.This is a left-tailed test.    This is a two-tailed test.

(b) What is the sample proportion of college binge-drinkers? Round your answer to 3 decimal places.
p̂ =

(c) What is the test statistic? Round your answer to 2 decimal places.
z =

(d) What is the P-value of the test statistic? Round your answer to 4 decimal places.
P-value =

(e) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(f) Choose the appropriate concluding statement.

There is enough data to justify rejection of the claim that half of all college students binge drink.There is not enough data to justify rejection of the claim that half of all college students binge drink.     We have proven that exactly one half of all college students binge drink.We have proven that the the claim is false.

Answer 1

a)This is a two-tailed test.

b)

sample proportion p̂ = x/n=240/450=

0.5330

c)

test stat z =(p̂-p)/√(p(1-p)/n)=

1.40 (please try 1.41 if this comes wrong)

d)

p value                          =

0.1616 (from excel: 2*(1-normsdist(1.40)) function )

(please try 0.1586 if this comes wrong)

e)

fail to reject H₀    

f)

.There is not enough data to justify rejection of the claim that half of all college students binge drink.