Principles of Econometrics ECMT 5001
Take-home Mid-semester Test
Principles of Econometrics代写 Using your answer to part (c), calculate the (i) expected value of s and (ii) variance of s.
Instructions:
Total marks: 26
Time permitted: 1.5 Hours
Permitted materials: Open Book.
This exam has 3 questions.
Answer all of the questions in this document.
Marks for each question are in parentheses [ ].
Show all workings and provide explanations for your answers.
State any assumptions that you need to make.
Prepare your answers in a separate document.
Good luck!
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 fifive 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] Principles of Econometrics代写
(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? [2 marks]
(c) What is the conditional probability of bowl C1 given that a red ball is drawn? [2 marks]
(d) What is the conditional probability of bowl C2 given that a red ball is drawn? [2 marks]
2.A statistics class taught by Karl Gauss provided the following examination grades for fifive students.A sample of two students is randomly selected without replacement. Principles of Econometrics代写
(a) Derive the sampling distribution of the mean number of grade points 
in the sample. [3 marks]
(b) Using your answer to part (a), calculate the (i) expected value of , and (ii) variance of . [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. Principles of Econometrics代写
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 α = 0.05 signifificance 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]
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