ECMT5001 Take-home Mid-semester 2021
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Principles of Econometrics ECMT 5001
Take-home Mid-semester Test
2021
1. It is known that bowl C1 contains 3 red and 7 blue balls and bowl C2 contains 8 red and 2 blue balls. All balls are identical in size and shape. A die is cast and bowl C1 is selected if five or six spots show on the side that is up; otherwise, bowl C2 is selected. The selected bowl is handed to another person and one ball is taken at random. Let C denote the event that a red ball is selected.
(a) (i) What is the probability that C1 is selected? (ii) What is the probability that C2 is selected?
[2 marks]
(b) (i) What is the conditional probability of the event C given that bowl C1 is selected? (ii) What
is the conditional probability of the event C given that bowl C2 is selected?
(c) What is the conditional probability of bowl C1 given that a red ball is drawn?
(d) What is the conditional probability of bowl C2 given that a red ball is drawn?
[2 marks] [2 marks] [2 marks]
2. A statistics class taught by Karl Gauss provided the following examination grades for five students. A sample of two students is randomly selected without replacement.
Name Grade Grade Points
|
Sigrid |
B |
3 |
|
Inge |
C |
2 |
|
Gustav |
B |
3 |
|
Hugo |
A |
4 |
|
Eva |
C |
2 |
(a) Derive the sampling distribution of the mean number of grade points X¯ in the sample. [3 marks] (b) Using your answer to part (a), calculate the (i) expected value of X¯ , and (ii) variance of X¯ ·
[2 marks]
(c) Derive the sampling distribution of the sample standard deviation s. [3 marks]
(d) Using your answer to part (c), calculate the (i) expected value of s and (ii) variance of s · [2 marks]
3. Jerzy Neyman is testing the null hypothesis that exactly half of all the undergraduate students in the Bachelor’s degree continue their formal education by taking courses within ten years of graduation. Using a sample of 200 persons, he found that 111 had taken course-work, within ten years after receiving their Bachelor’s degree.
(a) Formulate the null and alternative hypotheses. [2 marks] (b) He wishes to test the null hypothesis at the a = 0 ·05 significance level. Describe the test statistic you would use to conduct the test, compute the critical region for the test, and describe the decision rule you would use. [4 marks]
(c) Should Jerzy accept or reject the null hypothesis ? Express your answer as formal hypothesis testing conclusions. [2 marks]
2022-04-02