STA1502 TRIAL
EXAMINATIO
N PAPER 2022
(Questions and
Answers) Assume that you have a sample of n1 D 9; with the sample mean XN1 D 42 and a sample standard
deviation of S1 D 4; and you have an independent sample of n2 D 17 from another population with
a sample mean of XN2 D 34 and the sample s...
STA1502 TRIAL
EXAMINATIO
N PAPER 2022
(Questions and
Answers)
,1 TRIAL EXAMINATION PAPER
Question 1
Assume that you have a sample of n 1 D 9; with the sample mean XN1 D 42 and a sample standard
deviation of S1 D 4; and you have an independent sample of n 2 D 17 from another population with
a sample mean of XN2 D 34 and the sample standard deviation S2 D 5:
Test the hypothesis that the population mean for group 1 is greater than the population mean for
group 2.
Which one of the following statements is incorrect?
1. There are two independent populations and the test statistic is t–test.
2. The null nad alternative hypothesis are: H0 : 1 2 D 0 vs H1 : 1
> 2
:
3. The critical value at 1% level is 2:492:
4. The test statistic is 4:1375:
5. Do not reject H0 at the 1% level of significance.
Question 2
Consider the information on question 1, the 95% confidence interval estimate for the difference
between the two population means is
1. . 4:0092I 11:9908/
2. . 4:2103I 11:7897/
3. . 8I 3:7897/
4. . 4:0092I 10:9098/
5. . 11:9908I 4:0092/
Question 3
Suppose the necessary conditions are met, the population variances are known, and a two-tailed
test is being conducted to test the difference between two population means . 1 /
2 . Given the
following information
Sample A: n A D 30 XNA D 53:469 and 2
A D 374
Sample B: n B D 32 XNB D 48:625 and 2
B D 106
Test the hypothesis to determine if the population means are the same at D 0:05
2
, STA1502/103
Which one of the following statements is incorrect?
1. The pooled variance for the test statistic is not valid.
2. If the two populations are normally distributed than the difference between the two popula-
tions means is also normally distributed.
3. The standard error for the difference XNA XNB is 3:9723:
4. The rejection region is Z < 1:22 and Z > 1:22:
5. The test statistic Z D 1:2189:
Question 4
In testing whether the means of two normal populations are equal, summary statistics computed
for two independent samples are as follows:
Population
1 2
Sample size n 1 D 26 n 2 D 26
Sample mean xN1 D 7:30 xN2 D 6:80
Sample variance s12 D . 1:05/ 2 s22 D . 1:20/ 2
Assume that the population variances are equal. Which one of the following statements is incor-
rect?
1. The t–test statistic is appropriate
2. The rejection region at 5% is t > t. 50I0:05/ D 1:676
3. The standard error of XN1 XN2 D 0:3127
4. The critical value for a one–tailed test at 5% level of significance is 2:009
5. The 99% confidence interval for XN1 XN2 is . 0:3374I 1:3374/
Question 5
Six functionally illiterate adults were given an experimental one-week crash course in reading. Each
of the six adults was given a reading test prior to the course and another test after the course. The
results are shown below:
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