MATH312 Fall 2022 Practice Test II
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MATH312
Fall 2022
Practice Test II
A. Comprehensive Part
1. A study is being made on the failure of an electronic component. There are two types of failures (A and B) possible and two mounting positions (#1 and #2) for the device. The following data have been taken
Failure Type
A B 
Position-#1 
13 7
Position-#2 
6 14 
a.) Testing the significant association between “type of failure ”and “mounting position ”at 2.5% level by Chi-Square test. (note that H0 and H1 needs to be clearly specified)
b.) Construct the 97.5% confidence interval on the odds-ratio of failure type A for position-#1 to
position-#2. (30 .0125 = 2.24)
c.) Testing the same hypothesis as a.) in using odds-ratio and 2.5% level of significance. (Note that the
results from a.) to c.) are not necessarily consistent)
2. Given the following two samples independently drawn from two underlying Normal populations, you are asked to evaluate whether those two populations have the same centrality.
y
4.45
2.43
3.34
5.14
-2.22
3.73
0.25
0.70
0.05
2.83
a.) Testing on the equality of two population variances at 5% level.
b.) According to the result from a.), perform appropriate t-test for the equality of two population means
at 5% level.
c.) Ignoring the Normality assumption, use Wilcoxon rank test for the equality of two population means
at 5% level.
d.) Now, use two sample median test for the equality of two population medians at 5% level.
B. (20 points) Short Answer Problem. Only ONE answer for each of the multiple-choice problems should be attempted
( ) 1. Which of the following statement is TRUE?
a. If the sampling is with replacement, the variance of the sample average is smaller than or equal to the variance when the sampling is done without replacement.
b. According to Central Limit Theorem, no matter what underlying population is, when the sample size is large (≥ 30) the sample histogram is always bell-shaped.
c. t\-test is used for comparison of means when the variances of two independent population are equal.
d. F distribution is a continuous distribution for a random variable taking any real values.
e.
(2) (True/False) Nonparametric Wilcoxon rank test requires that the two populations whose means are to be tested have the distributions of the same shape and variation.
(3) The t-test statistics for H0 : u1 = u2 , H1 : u1 
u2 is equal to 3.876 with p-value at 0.02. Using the same data, what would be the p-value for testing H0 : u1 ≥ u2 , H1 : u1 < u2 ?
(4) It is reported that offspring of users of a certain recreational drug may have a higher incidence of birth defects than the general population. To obtain information about a possible relationship between this drug and birth defects, 100 offspring of female rats fed the drug and 100 offspring from untreated female rats are examined. It is found that the 95% confidence interval for the odds ratio for birth defects in the treated group compared to the untreated group (say o) is (1.417, 5.02). What is the conclusion of testing H0 : o s 1, H1 : o > 1 at a = 0.05?
5. A study to investigate the possible association between smoking behavior and squamous cell carcinoma for female was conducted. Adult females participated in the study and were grouped on the level of their tobacco consumption: light smoker (< 20 cig./day), heavy smoker (≥ 20 cig./day), and nonsmoker. The estimated odds ratio of the presence of squamous cell carcinoma for light smokers to heavy smokers equals 2.25; and the estimated odds ratio of the presence of squamous cell carcinoma for heavy smokers to nonsmokers equals 11.6. Find the estimated odds ratio of the presence of squamous cell carcinoma for light smoker to nonsmoker
2022-10-31