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TEST 2

SECOND SEMESTER, 2021/2022

Statistical Economics

ECN3221


Section A: Multiple Choice Questions (10 Marks)

Answer ALL questions.

1. The critical value of t for a two-tailed test with 6 degrees of freedom using α =

.05 is

a.

2.447.

b.

1.943.

c.

2.365.

d.

1.985.


2. When the following hypotheses are being tested at a level of significance of α

H0: μ 500

Ha: μ < 500

the null hypothesis will be rejected, if the p-value is

a.

α.

b.

> α.

c.

= α/2.

d.

1 - α/2.


3. In a two-tailed hypothesis test, the test statistic is determined to be z = -2.5. The

p-value for this test is

a.

.9876.

b.

.4938.

c.

.0062.

d.

.0124.


4. Read the t statistic from the t distribution table and circle the correct answer. For

a one-tailed test (lower tail), using a sample size of 10, and at the 10% level of significance, t =

a.

1.383.

b.

2.821.

c.

-1.383.

d.

-2.821.



5. Salary information regarding male and female employees of a large company is shown below.

Male

Female

Sample Size

64

36

Sample Mean Salary (in $1000)

44

41

Population Variance ()

128

72


The point estimate of the difference between the means of the two populations is

a.

-28.

b.

3.

c.

4.

d.

-4.




6. A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Today

Five Years Ago

82

88

σ2

112.5

54

n

45

36

The point estimate for the difference between the means of the two populations is

a.

58.5.

b.

9.

c.

-9.

d.

-6.


7. Which of the following has a chi-square distribution?

a.

(n - 1)σ2/s2.

b.

(n - 1)σ/s.

c.

(n - 1)s/σ.

d.

(n - 1)s2/σ2.


8. We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

a.

H0: σ2 < 1.44.

b.

H0: s2 1.44.

c.

H0: σ < 1.20.

d.

H0: σ2 1.44.


9. A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a.

100.75.

b.

10.

c.

51.25.

d.

50.


10. The value of F.01 with 9 numerator and 20 denominator degrees of freedom is


a.

2.39.

b.

2.94.

c.

2.91.

d.

3.46.





Section B: Short Answer Questions

Answer ALL questions.

Question 1 (20 Marks)

Recently, a local newspaper reported that part-time students are older than full-time students. In order to test the validity of its statement, two independent samples of students were selected.

Full-Time

Part-Time

(in years)

26

24

s

2

3

n

42

31

a.

Give the hypotheses for the above. (4 marks)

b.

Determine the degrees of freedom. (4 marks)

c.

Compute the test statistic. (6 marks)