Statistical Concept Preliminary Test
Please complete the following questions and return it to me by 11:59am (NOT PM) on the 27th
of Feb 2018. Top six students shall be chosen to compete in the actual stats exam.
Attention: Detailed steps are required for each and every question. Please make sure that your
steps are clear, organized and readable.
Name Maximum Your Score
Question 0 20
Question 1 20
Question 2 20
Question 3 20
Question 4 20
Question 5 20
Question 6 20
Total 20
Question 0 (20 points)
Please explain the following concept in your language. (4 points each)
a. t-test vs. z-test
b. p-value
c. confidence interval
d. practical vs. statistical significance
e. Stand Error (Please give the formula provided that the sample is large compared to the
population)
Question 1 (20 points)
How many 7-letter code words are possible using the letters in Kingdom if:
(a) The letters may be repeated. (2 points)
(b) The letters may not be repeated. (3 points)
(c) Only one letter can be repeated. (7 points)
(d) Two letters can be repeated. (8 points)
Question 2 (20 points)
There are 6 Stats questions, 4 Organizational Behavior(OB) questions and 5 Personal Finance
questions.
You pick them randomly to complete one by one. When you pick a Personal Finance question
and don’t like it, but you choose to still complete it. Once you pick the 2nd Personal Finance
question, you stop.
(1) What is the chance that you pick exactly 7 questions? (10 points)
(2) What is the expected number of questions that you pick? (5 points)
(3) What is the variance of the number of questions that you pick? (5 points)
Question 3 (20 points)
Kevin has 5 coins, two of which are double-headed, one double-tailed and two are fair coins
(one head one tail).
(a) Kevin closes his eyes, picks a coin at random and tosses it. What is the probability that the
upper side of the coin is a head? (5 points)
(b) Kevin now opens his eyes and sees that the coin has landed heads. What is the probability
that the lower face of the coin is a head? (5 points)
(c) Kevin now tosses the coin again and sees that it lands heads again. What is the probability
that the coin is double headed? (10 points)
Question 4 (20 points)
Kevin is grading exams of couple thousand students from YEAH. He takes a simple random
sample of 100 students and realizes that the average sore is 125, with an SD of 36.
(a) Using this information, can Kevin construct an approximate 90% confidence interval for the
average grade in his sample? If yes, please calculate and explain the confidence interval. If no,
then state the reason. (8 points)
(b) Using this information, can Kevin construct an approximate 90% confidence interval for the
average grade among all YEAH students? If yes, please calculate and explain the confidence
interval. If no, then state the reason. (8 points)
(c) Since the sample size is large enough, the central limit theorem says what is roughly normal
in this case? Please be specific. (4 points)
Question 5 (20 points)
After research, Kevin found out that 52.5% of all students at California Community Colleges
were male, while 47.5% were female. But Kevin believes that we have a higher percentage of
females in DVC than in the nation. He decides to perform. a statistical test.
(a) State the Kevin’s null and alternative hypotheses. What kind of test should he perform? (2
points)
(b) Kevin collects a simple random sample of 10,000 students’ bio information from DVC. He
finds that 48.55% of the interviewees were female. Draw (or describe) a box model to represent
this situation. Include information about the number and kind of tickets in the box, the number
and kind of draws, the composition of the sample, and what is done with the tickets. If any of
that information is unknown, indicate this. (4 points)
(c) Calculate the test statistics. (Hint: think carefully about what type of test you should perform)
(8 points)
(d) Calculate the p-value associated with this scenario. Use the context of the situation to make
a conclusion about the null hypothesis. (6 points)