Exam (elaborations)
STA1502 EXAM PACK 2024/2025 {QUESTIONS AND ANSWERS }
- Course
- Statistical Inference I
- Institution
- University Of South Africa
STA1502 EXAM PACK 2024/2025 {QUESTIONS AND ANSWERS }
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lOMoAR cPSD| 47715245Downloaded by palmer kamulee (kamuleepalmer@gmail.com)
, lOMoAR cPSD| 47715245
STA1502/204/0/2023
QUESTION 1 [4 marks]
Two population means that are normally distributed.
The summary statistics.
Sample Sample
1 2
Sample mean xN1 D xN2 D
D D
27:5 25:5
2 2
1. Correct Population D D
variance 89:2 78:4
2. Correct
1 2
3. Correct Sample size n1 25 n2 20
The standard error for the difference between two population means
when the population variances are known is
2 2
SE.xN1Nx2/D sn11 C n22
r89:2 78:4
D 25 C 20
D
p7:488
D
2:7364:
4. Correct
The test statistic for the difference between two population means is
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, lOMoAR cPSD| 47715245
D 2:7364
D 0:7309
5. Incorrect
XN1
XN2 Z D2 2
n11 C n22
D
The critical value at 5% level of significance is Z 2 D Z0:205 D Z0:025
D 1:96:
2
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STA1502/204/0/2023
Rule:
Reject the null hypothesis H0 if the test statistic Z is greater than the
critical value or when the p–value is less than (the level of
significance). Since the test statistic .0:7309/ is less than 1:96 (the
critical value), we fail to reject the null hypothesis H0 at the 5% level
of significance.
Option (5)
QUESTION 2 [4 marks]
The summary statistics are
Sample Sample
1 2
Sample mean XN1 D XN2 D
D D
27:5 25:5
2
The test Population D 2 D 78:4 statistic is Z D
0:7309: variance 89:2 2
Sample size 1 n2 20
The p-value D 2 n1 25 P .Z > 0:7309/ D
2 P .Z > 0:73/ D 2 0:2327 D 0:4674:
Option (1)
QUESTION 3 [4 marks]
The confidence interval for the difference between two population
means when the population variances are known.
The 90% confidence interval is
3
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