A survey on 1,500 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. Does this survey provide convincing evidence that the majority (more than 50%) of all high school seniors who take the SAT are fairly certain they will participate in a study abroad program in college?

Use a 0.05 level of significance. Hint: write the percentages as decimals.

1. What is the population of interest?

Group of answer choices

The 1500 seniors who took the SAT

All people in the united states

All high school seniors who took the SAT

All SAT Exams

2. What is the sample?

Group of answer choices

All high school seniors who took the SAT

All people in the United States

All SAT Exams

The 1500 seniors who took the SAT

3. What variable is being studied here?

Group of answer choices

The number of students who took the SAT

The optional web survey

How many study abroad opportunities are available

Whether or not the seniors who take the SAT will participate in a study abroad program in college

4. Describe the parameter of interest in words.

5. What is the value of the statistic for this study?

a) p^=0.55

b) =0.55

c) p^=0.5

d) =0.5

Group of answer choices

c

a

b

d

6. Set up the hypotheses for this study.

a)

Ho:=0.5

Ha:0.5

b)

Ho:=0.5

Ha:<0.5

c)

Ho:p^=0.55

Ha:p^>0.55

d)

Ho:=0.5

Ha:>0.5

Group of answer choices

b

a

c

d

7. Given the p-value is 0.01, would you reject or fail to reject the null hypothesis? Why?

8. Are validity conditions satisfied for using theory-based inference approach? Why or why not?

9. Compute the standardized statistic for the hypotheses in problem 6 using the theory-based approach. (Hint: I recommend you calculate the SD under the null first)

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10. Based on your standardized statistic you got in 9, what decision do you make? Hint: (Reject/Fail to Reject) the (null/alternative) hypothesis.

Does this agree with your decision you made based on the p value?

11. What does this conclusion mean in context of the problem?

12. Can we generalize the results of the study? If so, to whom can we generalize the results to? If not, explain why not.

Scenario 2:

It is believed that that average exam 1 score for all Stat 218 students at UNL is an 85. One professor decided to test to see if her students average was higher than the believed average. The average exam 1 score for the 25 students in her class was a 93 with a standard deviation of 23. The distribution of grades for her class was symmetric (not skewed).

1. What variable is studied here? Classify into categorical or quantitative.

2. Describe the parameter of interest in words. Give a symbol for it.

3. What is the value of the statistic for this study? Give a symbol for it.

a) =93

b) x=93

c) =93

d) p^=93

Group of answer choices

b

c

a

d

4. Write the hypotheses for this study in words.

5. Are validity conditions satisfied for using theory-based inference approach? Why or why not?

6. Compute the theory-based standardized statistic for this study.

7. What conclusion, in context of the study would you make?

8. Can we generalize the results of this study to all Stat 218 students at UNL? Why or why not?

9. What type of error could you have made in this scenario? Write the error in context.