Exam (elaborations)
STA1502 ASSIGNMENT 2 SOLUTIONS 2024
- Institution
- University Of South Africa (Unisa)
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Assessment 2Question 1
Many college and university students have obtained internship jobs. A statistics professor
wants to determine whether students in different degree programs earn different amounts. A
random sample of 4 students was selected in each of the department of Statistics,
Mathematics and Physics programs and they were asked to report how much they have
earned from the previous internship. The results (in R1000.00) are presented below.
Statistics Mathematics Physics
3.3 3.9 4.0
Data 2.5 5.1 6.2
4.6 3.9 6.3
5.4 6.2 5.9
The sample size 4 4 4
The sample mean 3.95 4.775 5.6
The sample variance 1.6833 1.2225 1.1667
To determine which population means differ in the internship earnings, the professor used the
least significant difference (LSD) method at 5% level of significance.
The calculated value of LSD is
Select one:
1. 1.8637.
2. 1.240.
3. 0.6515.
4. 2.179.
5. 1.420.
Question 2
A bank manager has been presented with 2 brochures, an old standard and a new
designed brochure that has to be more effective in attracting customers. Thirty five
percent (35%) of 200 of the customers were selected randomly to receive the old
standard brochure and 42% of 200 customers have received the new brochure. The
analyst wants to test whether the new developed brochure perform effectively better
than the old standard brochure at the 5% level of significance.
Which one of the following statements is incorrect?
Select one:
1. The null hypothesis H0 ∶ p1 - p2 = 0 and the alternative hypothesis H1 ∶ p1 - p2 > 0.
, 2. The sample proportions are 0.35 and 0.42, respectively.
3. The pooled proportion of p1 - p2 is 0.385.
4. The standard error of p1 - p2 is 0.0024.
5. The test statistic of p1 - p2 is - 1.4374.
Question 3
A PhD student has collected the data that represent the number of absences of lecturers
over the past academic year.
Absences of lecturers from the college as presented below:
Engineering Business Mathematics
X1 X2 X3
8 5 9
10 7 10
6 6 10
8 7 9
4 7 7
8 6 5
8 8 13
4 8 7
5 1 5
The one-way analysis of variance (ANOVA) is used to test the null hypothesis.
H0 : The population means are all equal.
Which one of the following statements is incorrect?
Select one:
1. The sample mean for the colleges are x ̅1 = 6.78, x 2̅ = 6.11 and x ̅3 = 8.33.
2. The sample variance for the colleges are s12= 4.44, s22 = 4.61, s 32= 6.75.
3. The sum square for treatment is 23.4067.
4. The sum square for error is 126.444.
5. The mean square for error is 4.986.
Question 4
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