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**

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