Assignment 7: Statistical Inference
Due at start of class on 6 March, 2006.

Name:

Each question is worth one half of one point unless otherwise indicated.

1. A random sample of 40 statistics students answered the question "How many hours per week do you spend studying statistics?" The mean value was 11.23 hours with a standard deviation of 2.41 hours. What is the lower limit of the 95% confidence interval?
2. What is the upper limit of the 95% confidence interval for the previous question?
3. What z-score corresponds to the 99% confidence interval?
(Be careful; the answer is not the z-score with area below of 0.99. If you are having problems, look at the area above the z-score for the 95% confidence interval (1.96) and at the area below the z-score for the other part of the 95% confidence interval (-1.96))
4. What is the lower limit of the 99% confidence interval for the data in question 1?
5. What is the upper limit of the 99% confidence interval for the data in question 1?
6. A professor wants to know if students who come to class have a larger number of points in the class compared to those who do not come to class regularly. Is this a one-tailed or two-tailed hypothesis? One Tailed Two Tailed
7. What is the null hypothesis for question 6? (Use u for μ; since you cannot subscript, just type the subscripted information normally.)
8. What is the alternative hypothesis for question 6?
9. A researcher wants to know if students who smoke have a higher or lower GPA than students who do not smoke. Is this a one-tailed or two-tailed hypothesis? One Tailed Two Tailed
10. What is the null hypothesis for question 9? (Use u for μ; since you cannot subscript, just type the subscripted information normally.)
11. What is the alternative hypothesis for question 9?
12. What is wrong with the following pair of hypotheses?
H0: μ1 = μ2
H1: μ1 > μ2
1. Nothing; they are fine.
2. They are not mutually exclusive of each other.
3. They are not exhaustive.
4. Both answers B and C.
13. What is wrong with the following pair of hypotheses?
H0: μ1 < μ2
H1: μ1 μ2
1. Nothing; they are fine.
2. They are not mutually exclusive of each other.
3. They are not exhaustive.
4. The null hypothesis must contain the equal sign.
14. What is wrong with the following pair of hypotheses?
H0: μ1 μ2
H1: μ1 μ2
1. Nothing; they are fine.
2. They are not mutually exclusive of each other.
3. They are not exhaustive.
4. Both answers B and C.
15. A researcher tries a new treatment with one group of participants, while another group does not receive the treatment. The treatment is effective, yet the statistical test failed to reject the null hypothesis. What type of error has been made?
1. Type-I error
2. Type-II error
16. A researcher concluded that a person's sex has an effect on GPA when in fact it does not. What type of error has been made?
1. Type-I error
2. Type-II error
17. (2 points) Explain why it is not possible to simultaneously reduce the likelihood of both Type-I and Type-II errors for a given sample size. It is not sufficient to state that as one goes up, the other goes down. The question asks why one goes up as the other goes down.