Midterm1 Sol
Stat 3022: Midterm Exam 1
March 5 (Tuesday), 2013
• Name:
• ID number:
• This exam must be your own work entirely. You can not talk to or share information with anybody. You are not allowed to share materials, and calculators.
• Cell phone must be turned off.
• You have 50 minutes to complete the exam.
1
Problem 1 (21 points total, 3 points each)
Choose one of the listed choices for each question (no explanation is needed), put your answers in the table on page 4.
1. Suppose you have a sample x1 , x2 , . . . , xn from a population. Which of the following has different unit as sample mean?
(A). population mean
(B). sample variance
(C). standard error
(D). single observation xi for i = 1, 2, . . . , n
2. In paired t-test with sample size n1 = n2 = 20, you have H0 : µ = 0 vs. Ha : µ < 0, the t-statistic is 3.4. what is the p-value?
(A).
1 - pt(3.4, 20)
(B).
1 - pt(3.4, 19)
(C).
pt(3.4, 20)
(D).
pt(3.4, 19)
3. Suppose y is response, x1 is numerical predictor, and x2 is categorical predictor with 2 levels. Which of the following R code will generate parallel line models?
(A).
lm(y ~ 1)
(B).
lm(y ~ x1)
(C).
lm(y ~ x1 + x2)
(D).
lm(y ~ x1 * x2)
4. In paired t-test with H0 : µ = 2, a 95% confidence interval for the mean of difference is (-0.035, 0.057). The corresponding t-test (two-sided Ha ) would:
(A). reject H0 at the α=0.05 significance level.
2
(B). fail to reject H0 at the α=0.05 significance level.
(C). can’t tell without more information.
5. For what type of experiment you can make causal inference, according to chapter
1 in the textbook?
(A). Randomized experiment
(B). Observational experiment
(C). Neither
(D). Both
6. In simple linear regression yi = β0 + β1 xi + i , where i = 1, 2, . . . , n. Define residual ei = yi − yˆi , where yˆi are fitted values. Which of the following is correct?
(A). E( i ) = 0
(B).
n i=1 i
=0
(C).
n i=1 ei
=0
(D). (A), (B), (C) are all wrong
7. In the following table, which cell corresponds to the type I
March 5 (Tuesday), 2013
• Name:
• ID number:
• This exam must be your own work entirely. You can not talk to or share information with anybody. You are not allowed to share materials, and calculators.
• Cell phone must be turned off.
• You have 50 minutes to complete the exam.
1
Problem 1 (21 points total, 3 points each)
Choose one of the listed choices for each question (no explanation is needed), put your answers in the table on page 4.
1. Suppose you have a sample x1 , x2 , . . . , xn from a population. Which of the following has different unit as sample mean?
(A). population mean
(B). sample variance
(C). standard error
(D). single observation xi for i = 1, 2, . . . , n
2. In paired t-test with sample size n1 = n2 = 20, you have H0 : µ = 0 vs. Ha : µ < 0, the t-statistic is 3.4. what is the p-value?
(A).
1 - pt(3.4, 20)
(B).
1 - pt(3.4, 19)
(C).
pt(3.4, 20)
(D).
pt(3.4, 19)
3. Suppose y is response, x1 is numerical predictor, and x2 is categorical predictor with 2 levels. Which of the following R code will generate parallel line models?
(A).
lm(y ~ 1)
(B).
lm(y ~ x1)
(C).
lm(y ~ x1 + x2)
(D).
lm(y ~ x1 * x2)
4. In paired t-test with H0 : µ = 2, a 95% confidence interval for the mean of difference is (-0.035, 0.057). The corresponding t-test (two-sided Ha ) would:
(A). reject H0 at the α=0.05 significance level.
2
(B). fail to reject H0 at the α=0.05 significance level.
(C). can’t tell without more information.
5. For what type of experiment you can make causal inference, according to chapter
1 in the textbook?
(A). Randomized experiment
(B). Observational experiment
(C). Neither
(D). Both
6. In simple linear regression yi = β0 + β1 xi + i , where i = 1, 2, . . . , n. Define residual ei = yi − yˆi , where yˆi are fitted values. Which of the following is correct?
(A). E( i ) = 0
(B).
n i=1 i
=0
(C).
n i=1 ei
=0
(D). (A), (B), (C) are all wrong
7. In the following table, which cell corresponds to the type I