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