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STA1502 EXAM PACK 2024
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- University Of South Africa (Unisa)
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STA1502EXAM PACK
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STA1502 OCTOBER NOVEMBER 2023
1 TRIAL EXAMINATION PAPER
Question 1
For a sample of 10 observations with a sample mean of 39 and sample standard deviation of 4. Let
assume that a second sample of size 7 is independent and from other population with a sample
mean of 37 and sample standard deviation of 3. Test the hypothesis that the population mean for
group 1 is greater than the population mean from group 2, which one of the following statement is
correct?
1. The population variance are known.
2. The alternative hypothesis is H1 : 1 < 2:
3. The critical value at 5% is 2:131.
4. H0 is not rejected at 5% level of significance.
5. The test statistic is 1:117:
Question 2
Using the information on question 1, the 95% confidence interval estimate for the difference be-
tween two population means is
1. .1:694I 5:694/
2. . 1:03269I 5:03269/
3. .1:03269I 5:03269/
4. . 1:69I 5:694/
5. . 1:81I 5:81/
Question 3
Given the folowing data:
Sample 1 Sample mean D 250 Sample standard deviation D 27 Sample size n 1 D 9
Sample 2 Sample mean D 238 Sample standard deviation D 15 Sample size n 2 D 9
Assume that the two samples are independent and normally distributed with unequal variances.
The test statistic for the difference between the two population means is
1. 12
2. 10:2956
3. 1:1655
4. 13:242
5. 1:1655
2
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STA1502/102/2/2020
Question 4
A paired difference experiment was conducted to compare the means of two populations:
Sample 1: 13 16 11 14 17
Sample 2: 12 15 11 12 18
The lecturer wants to determine if the population mean 1 differs from population mean 2. Which of
the following statements is incorrect?
1. The sample mean of the differences is 0:625:
2. The standard error of the difference is 0:4199:
3. The test statistic is 1:8844:
4. The critical value at 5% level is 2:365:
5. The confidence interval is . 0:3681I 1:6181/:
Question 5
Let assume that the population variance are known, and two tailed test is conducted to test the
difference between two population means . 1 2 / using the above information:
Sample 1: n 1 D 36 Mean X 1 D 69 2 D 360
1
Sample 2: n 2 D 49 Mean X 2 D 50 2 D 250
2
Test the hypothesis to determine if the population means are the same at D 0:05
Which one of the following statements is correct?
1. If the two populations are normally distributed then the difference between the two popula-
tions means is not normally distributed.
2. The standard error for the difference between the two means is 2:886:
3. The test statistic Z is 5:444:
4. The rejection region is Z is < 2:33 and Z is > 2:33:
5. We reject the null hypothesis at 5% level of significance
Question 6
The UNISA subjects tests in chemistry and Physics for two groups of 15 students each electing to
take these tests are given below.
Chemistry Physics
Mean D 629 Mean D 643
S1 D 110 S2 D 107
n 1 D 15 n 2 D 15
A statistician wants to determine if the variances are different? (use alpha = 5%). Which one of the
following statements is correct?
3
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1. A one-tailed test is appropriate.
2. The rejection is F < 2:89:
3. The test statistic F is 1:0569:
4. The lower confidence limit LC L D 0:5347:
5. The upper confidence limit U C L D 3:4196:
Question 7
An independent newspaper reported the result of a survey of 800 South Africans adults. The ques-
tion asked on the South Africans who were surveyed was” should SARS raised TAX on cigarettes
to pay for the health reform”. The result of the survey were summarizes as follows:
Smokers 195 were surveyed 41 said yes
Non-smokers 605 were surveyed 351 said yes
In testing if there is sufficient evidence to conclude at 5 % level of significance that the two popu-
lations ( smokers and non-smokers) differ significantly with respect to their opinions. Which one of
the following statement is correct?
1. The null and alternatives hypotheses are: H0 : p1 D p2 and p2 > p1 :
2. At 5% level of significance the rejection region is z < 1:96:
3. The p–value is 2:
4. The Z –statistic is 6:09:
5. The 95% confidence interval is .0:2935I 0:4463/.
Question 8
The following table gives numbers of democrats and republicans about their opinions on abortion.
Favor Indifferent Opposed Total
Democrats 138 83 64 285
Republicans 64 67 84 215
Total 202 150 184 500
Is there enough evidence to infer that the responses differ between the 2 groups at 5% level of
significance? Which one of the following statements is incorrect?
1. The variable are nominal for this test.
2. A chi-squared test of a contingency table is appropriate.
3. The test statistics is 22:152:
4. The degree of freedom is 2.
5. The rejection region at 5% level of significance is 2 > 6:99:
4
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