STA1502
EXAM PACK
+27 81 278 3372
,ADDENDUM B: SECOND SEMESTER ASSIGNMENTS
B.1 Assignment 01
ONLY FOR SEMESTER 2 STUDENTS
ASSIGNMENT 01
Unique Nr.: 784365
Fixed closing date: 31 August 2018
QUESTION 1
Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed
populations. Assume that the population variances are unknown but equal. In order to test the
difference between the population means, 1 2 , the sampling distribution of the sample mean
difference, x 1 x 2 , is
1. normally distributed
2. nonnormally distributed
3. t–distributed with 50 degrees of freedom
4. t–distributed with 48 degrees of freedom
5. F–distributed with 19 and 29 degrees of freedom
QUESTION 2
When testing H0: 1 2 D 0 against H1: 1 2 > 0; the observed value of the z–score was
found to be 2:15.
The p–value for this test would be
1. 0:0158
2. 0:0316
3. 0:9842
4. 0:0222
5. 0:9684
37
,QUESTION 3
Independent random samples of n 1 D 16 and n 2 D 13 observations were selected from two normal
populations with equal variances:
Population
1 2
Sample size 16 13
Sample mean 34:6 32:2
Sample variance 4:8 5:9
You wish to detect a possible difference between the population means. Which one of the following
statements is incorrect?
1. H0 : 1 2 D0 H1 : 1 2 6D 0
2. The rejection region for D 0:01 is 2:473
3. The test statistic is equal to 2:795
4. The null hypothesis is rejected at the 1% level of significance.
5. 1 > 2 at the 1% level of significance.
QUESTION 4
Thirty–five employees who completed two years of college were asked to take a basic mathematics
test. The mean and standard deviation of their scores were 75:1 and 12:8, respectively. In a random
sample of fifty employees who only completed high school, the mean and standard deviation of the
test scores were 72:1 and 14:6; respectively. Estimate with 90% confidence the difference in mean
scores between the two groups of employees.
1. LCL = 0:06 and UCL = 6:06
2. LCL = 12:58 and UCL = 18:58
3. LCL = 3:09 and UCL = 9:09
4. LCL = 2:99 and UCL = 8:99
5. LCL = 2:09 and UCL = 8:09
QUESTION 5
In testing for differences between the means of two dependent populations where the variance of
the differences is unknown, the degrees of freedom are
1. n D 1
2. n 1 C n 2 1
3. n 1 C n 2 2
4. n D 2
5. n D 1 1
38
, QUESTION 6
Which one of the following statements is incorrect?
1. In comparing two means when samples are dependent, the variable under consideration is
x D , where the subscript D refers to the difference.
2. The number of degrees of freedom, associated with the t–test, when the data are gathered
from a matched pairs experiment with 8 pairs, is 7.
3. A Marine drill instructor recorded the time in which each of 15 recruits completed an obstacle
course both before and after basic training. To test whether any improvement occurred, the
instructor would use a t–distribution with 15 degrees of freedom.
4. When comparing two population means, using data that are gathered from a matched pairs
experiment, the test statistic for D is Student t distributed with D n D 1 degrees of
freedom, provided that the differences are normally distributed.
5. In comparing two population means of interval data, we must decide whether the samples
are independent (in which case the parameter of interest is 1 2 ) or matched pairs (in
which case the parameter is D ) in order to select the correct test statistic.
QUESTION 7
To compare the wear of two types of automobile tyres, 1 and 2, an experimenter chose to “pair” the
measurements, comparing the wear for the two types of tyres on each of 7 automobiles, as shown
below.
Automobile 1 2 3 4 5 6 7
Tyre 1 8 15 7 9 10 13 11
Tyre 2 12 18 8 9 12 11 10
A statistician conducted a test to determine whether these data are sufficient to infer at the 10%
significance level that the two population means differ. Assume as correct that he tested H0: D D
0 against H1: D 6D 0; and calculated test statistics: t D 1:225 and rejection region jtj > t0:05;6 D
1:943: Below are statements referring to this testing, but one statement is incorrect. Identify the
incorrect statement:
1. Conclusion: Don’t reject the null hypothesis.
2. No, these data are not sufficient to infer at the 10% significance level that the two population
means differ.
3. We have enough information to estimate with 90% confidence the mean difference between
the two types of tyres.
4. This confidence interval will have LC L D 2:587, and U C L D 0:587.
5. Since the hypothesized value 0 is included in the 90% interval estimate, we reject the null
hypothesis at D 0:10.
39
EXAM PACK
+27 81 278 3372
,ADDENDUM B: SECOND SEMESTER ASSIGNMENTS
B.1 Assignment 01
ONLY FOR SEMESTER 2 STUDENTS
ASSIGNMENT 01
Unique Nr.: 784365
Fixed closing date: 31 August 2018
QUESTION 1
Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed
populations. Assume that the population variances are unknown but equal. In order to test the
difference between the population means, 1 2 , the sampling distribution of the sample mean
difference, x 1 x 2 , is
1. normally distributed
2. nonnormally distributed
3. t–distributed with 50 degrees of freedom
4. t–distributed with 48 degrees of freedom
5. F–distributed with 19 and 29 degrees of freedom
QUESTION 2
When testing H0: 1 2 D 0 against H1: 1 2 > 0; the observed value of the z–score was
found to be 2:15.
The p–value for this test would be
1. 0:0158
2. 0:0316
3. 0:9842
4. 0:0222
5. 0:9684
37
,QUESTION 3
Independent random samples of n 1 D 16 and n 2 D 13 observations were selected from two normal
populations with equal variances:
Population
1 2
Sample size 16 13
Sample mean 34:6 32:2
Sample variance 4:8 5:9
You wish to detect a possible difference between the population means. Which one of the following
statements is incorrect?
1. H0 : 1 2 D0 H1 : 1 2 6D 0
2. The rejection region for D 0:01 is 2:473
3. The test statistic is equal to 2:795
4. The null hypothesis is rejected at the 1% level of significance.
5. 1 > 2 at the 1% level of significance.
QUESTION 4
Thirty–five employees who completed two years of college were asked to take a basic mathematics
test. The mean and standard deviation of their scores were 75:1 and 12:8, respectively. In a random
sample of fifty employees who only completed high school, the mean and standard deviation of the
test scores were 72:1 and 14:6; respectively. Estimate with 90% confidence the difference in mean
scores between the two groups of employees.
1. LCL = 0:06 and UCL = 6:06
2. LCL = 12:58 and UCL = 18:58
3. LCL = 3:09 and UCL = 9:09
4. LCL = 2:99 and UCL = 8:99
5. LCL = 2:09 and UCL = 8:09
QUESTION 5
In testing for differences between the means of two dependent populations where the variance of
the differences is unknown, the degrees of freedom are
1. n D 1
2. n 1 C n 2 1
3. n 1 C n 2 2
4. n D 2
5. n D 1 1
38
, QUESTION 6
Which one of the following statements is incorrect?
1. In comparing two means when samples are dependent, the variable under consideration is
x D , where the subscript D refers to the difference.
2. The number of degrees of freedom, associated with the t–test, when the data are gathered
from a matched pairs experiment with 8 pairs, is 7.
3. A Marine drill instructor recorded the time in which each of 15 recruits completed an obstacle
course both before and after basic training. To test whether any improvement occurred, the
instructor would use a t–distribution with 15 degrees of freedom.
4. When comparing two population means, using data that are gathered from a matched pairs
experiment, the test statistic for D is Student t distributed with D n D 1 degrees of
freedom, provided that the differences are normally distributed.
5. In comparing two population means of interval data, we must decide whether the samples
are independent (in which case the parameter of interest is 1 2 ) or matched pairs (in
which case the parameter is D ) in order to select the correct test statistic.
QUESTION 7
To compare the wear of two types of automobile tyres, 1 and 2, an experimenter chose to “pair” the
measurements, comparing the wear for the two types of tyres on each of 7 automobiles, as shown
below.
Automobile 1 2 3 4 5 6 7
Tyre 1 8 15 7 9 10 13 11
Tyre 2 12 18 8 9 12 11 10
A statistician conducted a test to determine whether these data are sufficient to infer at the 10%
significance level that the two population means differ. Assume as correct that he tested H0: D D
0 against H1: D 6D 0; and calculated test statistics: t D 1:225 and rejection region jtj > t0:05;6 D
1:943: Below are statements referring to this testing, but one statement is incorrect. Identify the
incorrect statement:
1. Conclusion: Don’t reject the null hypothesis.
2. No, these data are not sufficient to infer at the 10% significance level that the two population
means differ.
3. We have enough information to estimate with 90% confidence the mean difference between
the two types of tyres.
4. This confidence interval will have LC L D 2:587, and U C L D 0:587.
5. Since the hypothesized value 0 is included in the 90% interval estimate, we reject the null
hypothesis at D 0:10.
39
