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STA3024 Exam2 Practice 2 solutions
Intro To Statistics 2 (STA 3024)
University of Florida
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STA 3024 Practice Exam 2
COVER SHEET
(Should be completed IN INK)
Student NAME:________________________________________
UFID#: ________________________________________
"On my honor, I have neither given nor received unauthorized aid on this examination.”
Signature: _________________________ Date:
Signature (Proctor):
FILL OUT your personal information at the top of the COVER SHEET and the FIRST PAGE of the exam IN INK. GET the signature of the instructor (or proctor) when you SUBMIT the test. DETACH the cover sheet and KEEP it until the grades are posted. You WILL NOT HAVE ANY ACCESS to your test-related data without this cover sheet.
Critical value:
Models (This can be extended to the general cases depending on the context)
Linear regression model:
Polynomial regression model:
Exponential regression model:
Logistic regression model: where
Chi-squared distribution with df has mean = df and sd=
Comparing two means w. the “same sd” assumption
95% CI for where.
Comparing two means among groups with the total sample size of with the “same sd” assumption
95% CI for where.
Within-groups estimate of =
Between-groups estimate of =
Bonfferoni method construct CI for each comparison where to achieve overall confidence level.
The conditional probability of A given B: P(A|B)
If events A and B are independent, P(A&B)=P(A)*P(B)
Chi-squared statistic:
STA 3024 Practice Exam 2 NAME:________________________________________ (IN INK)
UFID#: ________________________________________ "On my honor, I have neither given nor received unauthorized aid on this examination” Signature: _________________________
INSTRUCTIONS: FORMAT: This exam contains X questions. Each question is worth X points, for a total of X points. You can get the maximum of 100 points from this exam. TIME: You will have 60 minutes to complete the exam. ANSWERS: Select the BEST answer among the alternatives given. Only the answers bubbled in the scantron sheet will be graded. YOU MUST SUBMIT THIS TEST to the instructors together with the scantron sheet when you are finished. You may DETACH THE FORMULA SHEET and THE SCATCH PAPERS.
---------------------------------------------------After this line, either pencil or pen can be used---------------------------------------------------
[1-3] Suppose we have the following summary statistic: Group 1 Group 2 Overall Sample mean
8 10 9
Sample var 4 6 Sample size 5 5 10
- Suppose we believe that all groups share the same standard deviation. Find the within-groups estimate of the common variance.
(4+6)/2 = 5
Find the between-groups estimate of the common variance.
Construct 95% CI for.
[4-6] Suppose we want to compare mean exam scores by majors. We obtained the following ANOVA table: Source df SS MS F-stat
Major 10 55 5. Error 15 45 3 Total 25 100
- Find the number of categories in Major.
11
- Find the between-group variability estimate.
55/10=5.
- Conduct the F test and determine if the p-value is less than 0.
p-value < 0. Reject the null hypothesis of no difference between group means.
[7-8] Suppose we want to test whether the mean corn yield is the same for 5 types of fertilizer with the total sample size. Fertilizer 1 Fertilizer 2 ...
3 2
6 2
4 3
1 1
1
Suppose the within-group variability estimate. Find the 95% CI for using the Fisher method assuming the same standard deviation for each group.
Find the individual confidence level using the Bonfer- roni method to achieve 95% overall confidence.
[9] Suppose we have two factors (Major and Level) and want to conduct the two-way ANOVA.
- Under no interaction, the estimated GPA from the linear regression model is summarized in the table below. Find the estimated mean GPA when Level=Senior and Major=Stat (grey block). Maj. Lv.
Stat Math Others
Freshman 3 3. Sophomore 2 3. Junior Senior 3.
Others -> Stat: 2.9-3=-0. Freshman -> Senior: 3.5-3=+0. Freshman & Stat = 3.5-0=3. Senior & Stat = 3+0=3.
[10-12] We are interested in the relationship between satisfaction (Satisfied and Not satisfied) and price (High and Low) for a service. We observed the following contingency table.
Satisfied Not satisfied Total High 55 5 60 Low 25 15 40 Total 80 20 100
- Find the test statistic for the test of independence and conduct the test.
Expected cell counts: S N Total High 48 (0*0=0. )
12
(0*0=0.
)
60
Low 32 (0*0=0. )
8
(0*0=0.
)
40
Total 80 20 100
- Find the ratio of proportions (relative risk) of being satisfied. (High in the numerator)
Conditional probs: S N High 55/60 5/ Low 25/40 15/
[13] Suppose we want to compare the effect of Treatment 1 and 2. We observe 10 subjects who are assigned to both Trt 1 and 2 in a random order. Scores are recorded as follows (0-10 scale, 10 is the best): ID Trt 1 Trt 2 1 4 7 2 2 3 3 5 3 4 4 9 5 10 1 6 9 10 7 3 8 8 7 8 9 3 2 10 6 7
Give an example of the case that supports : “Treatment 1 is better than Treatment 2” than our observation?
Eg. The case where Trt 1 is better for all subjects.
STA3024 Exam2 Practice 2 solutions
Course: Intro To Statistics 2 (STA 3024)
University: University of Florida
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