STAT 200 QUIZ

STAT 200    Fall 2017

Quiz #3

Answer all 20 questions.  Each question is worth 4 points, and the maximum score for the quiz is 80 points.  Make sure your answers are as complete as possible and show your work/argument.  In particular, when there are calculations involved, you should show how you come up with your answers with critical work and/or necessary steps. The quiz is due by 11:59 PM, Sunday, October 8th, Eastern Standard Time.

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1. Conventionally, we will fail to reject the null hypothesis if the probability value is:

a. Greater than or equal to 0.05

b. Less than 0.05

c. Less than 0.01

d. Less than 0.95

2. A teacher assumed there was a correlation between amount of hours that his students studied before a history class and their grades. The null hypothesis was that the correlation between the study hours and grades was:

a. Positive 1.0

b. Negative 1.0

c. Zero

d. Positive 0.50

3. Which of the following can increase the rate of Type I error? (select all that apply)

a. Adjusting the significance level from 0.01 to 0.05

b. Adjusting the significance level from 0.05 to 0.01

c. Adjusting the significance level from 0.10 to 0.05

d. Adjusting the significance level from 0.05 to 0.10

4. At which of the following significance levels do you feel the most confident to reject the null hypothesis?

a. 0.05

b. 0.01

c. 0.95

d. 0.99

5. A teacher hypothesized that the on average, his students consumed two bottles of soda per day. Imagine that the teacher recorded soda consumption for every student: the confidence interval of soda consumption was (1.6, 2.4). Can you reject the teacher’s null hypothesis at 95%?

a. Yes

b. No

c. We cannot tell from the given information

6. If a statistical test result is significant at the 0.01 level, then we can conclude:

a. It is not significant at 0.05 level

b. It is not significant at 0.10 level

c. We do not know if it will be significant at 0.05 level

d. It must be significant at 0.05 level

7. ___ is the probability of accepting a false null hypothesis.

a. 1-β

b. β

c. α

d. 1- α

8. A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled six students in his class and recorded the number of minutes that they exercised in the past day. The numbers were 30mins, 40 mins, 60 mins, 80 mins, 20 mins, and 85 mins. What’s the sample standard deviation ? (show work)

9. A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled six students in his class and recorded the number of minutes that they exercised in the past day. The numbers were 30mins, 40 mins, 60 mins, 80 mins, 20 mins, and 85 mins. This teacher posed a null hypothesis that the average amount of physical activity of his students should be 60 mins per day. What is the absolute value of calculated t that we use for testing the null hypothesis? (show work)

10. Which of the following descriptions about t distribution is correct (select only one)?

a. Compared to the normal distribution, the t distribution has more values at the top and fewer at the tail.

b. Compared to the normal distribution, the t distribution has fewer values at the top and more values at the tail.

c. T distribution always has the same shape with a normal distribution

d. T distribution is extremely right-skewed

11. A professor posed a hypothesis that there was no significant difference between boys and girls on their soda consumption per day in an elementary school. He randomly sampled 25 boys and 25 girls. The mean soda consumption for boys was 40 oz per day and the standard deviation was 5. The mean soda consumption for girls was 30 oz per day and the standard deviation was 5. What is the standard error of the difference in means? (show work)

12. We can use pairwise comparison if we want to compare the means between the average GPA in 8 different schools.

a. Yes

b. No

13. A professor wants to test all possible pairwise comparisons among all four means. If we need to maintain an “experiment–wise” alpha of 0.01, what is the error rate per comparison after applying Bonferroni correction? (show work)

14. The value of t will increase as the standard deviation of difference___ and the difference between means___.

a. Increases; decreases

b. Increases; Increases

c. Decreases; decreases

d. Decreases; Increases

15. 1-β is the probability of_______

a. Rejecting a true null hypothesis

b. Accepting a true null hypothesis

c. Accepting a false null hypothesis

d. Rejecting a false null hypothesis

16. If the probability that you will correctly reject a false null hypothesis is 0.80 at 0.10 significance level, α is__ and power is__.

a. 0.10, 0.20

b. 0.10, 0.80

c. 0.90, 0.20

d. 0.99, 0.80

17. If the significance level changes from 0.05 to 0.01, the power will___

a. Increase

b. Decrease

c. Stay the same

d. First increase, then decrease

18. Which of the following descriptions are correct?

a. Increasing sample size from 5 to 25 will increase power to a greater degree than increasing sample size from 15 to 35.

b. Increasing sample size from 60 to 80 will increase power to the same degree as increasing sample size from 200 to 220.

c. Increasing sample size from 40 to 60 will decrease power to a greater degree than increasing sample size from 60 to 80.

d. Increasing sample size from 50 to 70 will decrease power to the same degree as increasing sample size from 70 to 90.

19. Which of the following descriptions are correct regarding power (select all that apply)?

a. Changing from a one-tailed test to a two-tailed test can increase power

b. Increasing sample size can increase power

c. Increasing standard deviation will decrease power

d. Changing from a one-tailed test to a two-tailed test, or changing from a two-tailed test to a one-tailed test will not change power

20. Which of the following are correct (select all that apply)?

a. Researchers need to be aware that there is a tradeoff between significance level and power

b. Researchers can increase power of experiments by increasing sample size

c. Researchers can increase power of experiments by increasing significance level