Question

(1 point)

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 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.

What are the hypotheses?
_?0:?>0.5,??:?=0.5

_?0:?=0.5,??:?>0.5
_?0:?=0.5,??:?≠0.5
_?0:?=0.5,??:?<0.5
_?0:?<0.5,??:?=0.5

Is the independence condition met?

_yes or no or no enough information

Is the success-failiure condition met?

_yes or no or no enough information

What is the value of the test statistic?
(Please answer to 2 decimal places and watch your signs)

What is the p-value?
(Please answer to 4 decimal places)

Interpret the p-value in this context.
_We reject ?0: less than half of American adults who decide not to go to college make this decision because they cannot afford college
_We reject ?0: half of American adults who decide not to go to college make this decision because they cannot afford college
_We fail to reject ?0: less than half of American adults who decide not to go to college make this decision because they cannot afford college
_We fail to reject ?0: half of American adults who decide not to go to college make this decision because they cannot afford college

Interpret the interval in this context. Does the confidence interval agree with the conclusion of the hypothesis test?
a_Yes, since we failed to reject the null hypothesis
b_Yes, since we rejected the null hypothesis
c_No, since we failed to reject the null hypothesis
d_No, since we rejected the null hypothesis

2.

Is college worth it? Part II Results of a poll of 331 Americans say that 48% who decide to not go to college do so because they cannot afford it. Assume that the distribution is approximately normal.

What would the lower end of a 90% confidence interval be?
(Please answer to 3 decimal places)

What would the upper end of a 90% confidence interval be?
(Please answer to 3 decimal places)

Which of the following can be concluded from the confidence interval?
__We may reject the null hypothesis
__We fail to reject the null hypothesis

Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
(Please answer to the nearest whole number)

Answer 1

Ans:

?₀:?=0.5,?_?:?<0.5

yes, independence condition met

yes,success-failure condition met

Test statistic:

z=(0.48-0.5)/SQRT(0.5*(1-0.5)/331)

z=-0.73

p-value=P(z<-0.728)=0.2333

Correct option is:

We fail to reject ?0: half of American adults who decide not to go to college make this decision because they cannot afford college

Yes, since we failed to reject the null hypothesis

90% confidence interval for proportion

=0.48+/-1.645*sqrt(0.48*(1-0.48)/331)

=0.48+/-0.045

=(0.435, 0.525)

lower end of a 90% confidence interval=0.435

upper end of a 90% confidence interval=0.525

We fail to reject the null hypothesis(as, confidence interval contain 0.5 within its limits)

Sample size required,n=1.645^2*0.48*(1-0.48)/0.015^2=3002