Instructions
Instructions
Instructions
5/12/2019
Name:
Student ID:
Section:
Instructor’s Name:
Instructions
1. Fill in your name, ID number, Instructor’s name, and Section number above.
2. Please do not turn over to next pages until you are told to do so.
3. This examination consists of 5 (multipart) questions and 7 pages including this page without tables. You have 60
minutes to finish this exam. Please manage your time according to the number of points allocated for each question as
shown in the table below.
4. Try to answer all questions. Show your work whenever possible. Explanation should be brief. Good luck.
1
Question 1 (10 points)
1. Probability distribution of a statistics is called:
(a) Sampling
(b) Parameter
(c) Data
(d) Sampling distribution
2. Standard deviation of sampling distribution of a statistic is called:
4. A numerical value used as a summary measure for a sample, such as sample mean, is known as
(a) a population parameter
(b) sample parameter
(c) sample statistic
(d) population mean
5. A tabular summary of a set of data showing the fraction of the total number of items in several classes is a
(a) frequency distribution
(b) relative frequency distribution
(c) frequency
(d) cumulative frequency distribution
6. A student takes a standardized exam. The grader reports the student’s standardized score (z-score) as –1.8. This
indicates:
2
7. You take a random sample from some population and form a 96% confidence interval for the population mean, Which
quantity is guaranteed to be in the interval you form?
(a) 0
(b) µ
(c) X̄
(d) 0.96
8. Decreasing the sample size, while holding the confidence level the same, will do what to the length of your confidence
interval?
10. X is normally distributed with known standard deviation. The margin of error associated with a 90% confidence
interval for is
(a) 1.28 √σ
n
3
Question 2 (10 points)
1. A police officer is interested in the drug and alcohol use of all high school students. He goes to his local high school to
question some of the students.
(a) Suppose the officer initially decides to question students by asking them face-to-face. If a student does not want
to tell the officer the truth and simply declares himself drug-free, what error is introduced into the study?
i. Sampling error
ii. Non-Sampling error
(b) Suppose the officer grabs a random sample but only does so of the freshman students. What type of error does
this study suffer from?
i. Sampling error
ii. Non-Sampling error
(c) Suppose the officer distributes anonymous surveys to 100 random high school students but only receives 12 of the
surveys back. What type of error does this study suffer from?
i. Sampling error
ii. Non-Sampling error
(d) A surveyor mistakenly records answers to one question in the wrong space. What type of error does this study
suffer from?
i. Sampling error
ii. Non-Sampling error
2. Identify the sampling technique used (random, cluster, stratified):
(a) 32 sophomores, 35 juniors and 49 seniors are randomly selected from 230 sophomores, 280 juniors, 577 seniors at
a certain high school.
(b) Calling randomly generated telephone numbers, a study asked 855 U.S. adults which medical conditions could be
prevented by their diet.
(c) A pregnancy study in Chicago, randomly selected 25 communities from the metropolitan area, then interviewed
all pregnant women in these communities.
(d) Select three students from a class to receive ice cream by putting all the students’ names in a hat and picking out
three names randomly.
(b) To determine whether a review session will improve his students’ test scores, a Stat 113 instructor divides his
class into two groups. He then requires one group to attend a study session and compares the test results of each
group.
4
Question 3 (10 points)
A random sample of size 16 is taken from a normal population having a mean of 100 and a variance of 4.
1. What is the sampling distribution of X̄? Expalin why?
4. What is the probability that the sample mean X̄ is between 75 and 90?
5
Question 4 (10 points)
The weight of bags of red balls follows a normal distribution with a mean of 25.8kg and a standard deviation of of 0.5kg.
1. What is the mode of the weight of the bags?
2. Determine the probability that a randomly selected bag of red balls will weigh
(a) less than 25kg
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Question 5 (10 points)
1. A sample of size n = 100 produced the sample mean of X̄ = 16. Assuming the population standard deviation σ = 3,
(a) What is the point estimator for µ?