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

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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

Expert Solution
Step 1

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 p^=0.48.

(a) 

The statistical hypothesis that will be formed to support the newspaper article is:

H0: p=0.5(p0)

H1: p0.5

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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