Question

6.16 Is college worth it? Part I: Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.


(a) A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement.
The hypotheses for this test are:

• Ho: p = .5
  Ha: p < .5
• Ho: p = .5
  Ha: p ≠ .5
• Ho: p = .5
  Ha: p > .5

The test statistic is:  (please round to two decimal places) The p-value associated with this hypothesis test is:  (please round to four decimal places) What is the conclusion of the hypothesis test?

• Since p<α we fail to reject the null hypothesis
• Since p<α we reject the null hypothesis and accept the alternative
• Since p ≥ α we do not have enough evidence to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis
• Since p ≥ α we reject the null hypothesis and accept the alternative

Interpret the result of the test in the context of this study and article:

• The data provide sufficient evidence to claim that only a minority of Americans who choose not to go to college do so because they cannot afford it
• The data do not provide sufficient evidence to claim that only a minority of Americans who choose not to go to college do so because they cannot afford it

(b) Would you expect a confidence interval for the proportion of American adults who decide not to go to college because they cannot afford it to include 0.5?

• yes
• no

Answer 1

a)

Ho: p = .5
Ha: p < .5

std error   se =√(p*(1-p)/n) =		0.0275
sample proportion p̂ = x/n=		0.4800

test stat z =(p̂-p)/√(p(1-p)/n)=		-0.73
p value                          =		0.2327

Since p ≥ α we do not have enough evidence to reject the null hypothesis

The data do not provide sufficient evidence to claim that only a minority of Americans who choose not to go to college do so because they cannot afford it

b)

Yes