IMathAS-libretexts

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

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