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 fail 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 ( ) Since p ≥ α we do not have enough evidence to reject the null hypothesis 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
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 fail 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
( ) Since p ≥ α we do not have enough evidence to reject the null hypothesis
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
Given:
The sample number of American adults is n=331.
The proportion of adults who decided not to go to college because they could not afford school is .
(a)
The statistical hypothesis that will be formed to support the newspaper article is:
H0:
H1:
where p is the true representative of the population proportion of adults who decided not to go to college because they could not afford school.
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