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 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 fail to reject 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 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
• 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

(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?

• no
• yes

Answer 1

Answer:

a)

Given,

Null hypothesis Ho : p = 0.5

Alternative hypothesis Ha : p < 0.5

sample size n = 331

p^ = 48% = 0.48

test statistic z = (p^ - p)/sqrt(pq/n)

substitute values

= (0.48 - 0.5)/sqrt(0.5*0.5/331)

z = - 0.73

Corresponding p value = P(z < -0.73)

= 0.2326951 [since from z table]

p value = 0.2327

Here we observe that, p value is high , so we fail to reject Ho.

So there is no sufficient evidence to support the statement that only a minority of the Americans who decide not to go to college do so because they cannot afford it.

b)

Here we don't reject Ho, so the confidence interval for the proportion of American adults may lies & it includes 0.5 which is within the limits