Question

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?

a. Since p<? we fail to reject the null hypothesis

b. Since p<? we reject the null hypothesis and accept the alternative

c. Since p ? ? we accept the null hypothesis

d. Since p ? ? we do not have enough evidence to reject the null hypothesis

e. Since p ? ? we reject the null hypothesis and accept the alternative

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

a. 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. 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?

a. yes

b. no

Answer 1

here as level of significance is not given we consider it as 0.05

null Hypothesis alternate Hypothesis: Ho: 0.5000 Ha: 0.5000 for 0.05 level with left tailed test, critical value of Decision rule 1.6449 reject Ho if test statisticz < -1.645 sample success 159 331 sample size std error -Se 0.0275 sample proportion p 0.4800 test stat Z (p-p)/Se- 0.728 p value 0.2334

Ho: p = .5
Ha: p < .5

The test statistic is: =-0.73

The p-value associated with this hypothesis test is: 0.2327

since p value is greater than alpha we do not have enough evidence to reject the null hypothesis

a. 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)

a. yes