Question

6.16 Is college worth it? Part I: Among a simple random sample of 331 American adults...

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

Homework Answers

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

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