Stat 200 Final Exam –
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STAT 200 FINAL EXAM – Complete Solution
1. True or False. Justify for full credit.
(a) The volume of milk in a jug of milk is 128 oz. The value 128
is from a discrete data set.
(25 pts)
·
(b)
If the variance from a data set is zero, then all the observations in
this data set must be zero.
·
(c)
P( A AND Ac ) 0, where Ac is the complement of A.
·
(d)
The mean and median for a normal distribution are always the same.
·
(e)
In a hypothesis testing, if the p-value is less than the significance
level α, we do not
have sufficient evidence to reject the null
hypothesis.
Refer to the following frequency distribution for Questions 2,
3, 4, and 5. Show all work. Just the answer, without supporting work, will
receive no credit.
A random sample of 25 customers was chosen in UMUC MiniMart
between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution
below shows the distribution for checkout time (in minutes).
|
Checkout Time (in minutes)
|
Frequency
|
Relative Frequency
|
|
1.0 – 1.9
|
6
|
|
|
2.0 – 2.9
|
8
|
|
|
3.0 – 3.9
|
||
|
4.0 – 5.9
|
5
|
|
|
Total
|
25
|
2. Complete the frequency table with frequency and relative
frequency.
3. What percentage of the checkout times was less
than 3 minutes?
4. In what class interval must the median lie?
Explain your answer.
5. Assume that the largest observation in this
dataset is 5.8. Suppose this observation were
incorrectly recorded
as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same?
Will the median increase, decrease or remain the same? Why? (5 pts)
Refer to the following information for Questions 6, 7, and 8.
Show all work. Just the answer, without supporting work, will receive no
credit.
A 6-faced die is rolled two times. Let A be the event that the
outcome of the first roll is an even number, and B be the event that the
outcome of second roll is greater than 4.
6. How many outcomes are there in the sample
space? (5 pts)
7. What is the probability that the outcome of
the second roll is greater than 4, given that the first roll is an even number?
(10 pts)
8. Are A and B independent? Why or why not?
Refer to the following situation for Questions 9, 10, and 11.
The five-number summary below shows the grade distribution of
two STAT 200 quizzes.
|
Minimum
|
Q1
|
Median
|
Q3
|
Maximum
|
|
|
Quiz 1
|
12
|
40
|
60
|
95
|
100
|
|
Quiz 2
|
20
|
35
|
50
|
90
|
100
|
For each question, give your answer as one of the following: (a)
Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is
impossible to tell using only the given information. Then explain your answer
in each case. (5 pts each)
9. Which quiz has less interquartile range in
grade distribution?
10. Which quiz has the greater percentage of
students with grades 90 and over?
11. Which quiz has a greater percentage of
students with grades less than 60?
Refer to the following information for Questions 12 and 13. Show
all work. Just the answer, without supporting work, will receive no credit.
There are 1000 juniors in a college. Among the 1000 juniors, 200
students are taking STAT200, and 100 students are taking PSYC300. There are 50
students taking both courses.
12. What is the probability that a randomly
selected junior is taking at least one of these two courses? (10 pts)
13. What is the probability that a randomly
selected junior is taking PSYC300, given that he/she is taking STAT200? (10
pts)
14. UMUC Stat Club is sending a delegate of 2
members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10
qualified candidates. How many different ways can the delegate be
selected?
15. Imagine you are in a game show. There are 4
prizes hidden on a game board with 10 spaces. One prize is worth $100, another
is worth $50, and two are worth $10. You have to pay $20 to the host if your
choice is not correct. Let the random variable x be the winning. Show all work.
Just the answer, without supporting work, will receive no credit.
1.
What
is your expected winning in this game?
2.
Determine
the standard deviation of x. (Round the answer to two decimal places.)
16. Mimi just started her tennis class three weeks ago. On
average, she is able to return 20% of her opponent’s serves. Assume her
opponent serves 8 times. Show all work. Just the answer, without supporting
work, will receive no credit.
(a) Let X be the number of returns that Mimi gets. As we know,
the distribution of X is a binomial probability distribution. What is the
number of trials (n), probability of successes (p) and probability of failures
(q), respectively?
·
(b)
Find the probability that that she returns at least 1 of the 8 serves
from her opponent.
·
(c)
How many serves can she expect to return?
Refer to the following information for Questions 17, 18, and 19.
Show all work. Just the answer, without supporting work, will receive no
credit.
(5 pts) (10 pts) (5 pts)
The heights of pecan trees are normally distributed with a mean
of 10 feet and a standard deviation of 2 feet.
17. What is the probability that a randomly
selected pecan tree is between 10 and 12 feet tall? (10 pts)
18. Find the 3rd quartile of the pecan tree height
distribution. (5 pts)
19. If a random sample of 100 pecan trees is
selected, what is the standard deviation of the sample mean?
20. A random sample of 225 SAT scores has a sample
mean of 1500. Assume that SAT scores have a population standard deviation of
300. Construct a 95% confidence interval estimate of the mean SAT scores. Show
all work. Just the answer, without supporting work, will receive no credit.
21. Consider the hypothesis test given by
8. 0:p 0.5
8. 1:p 0.5
In a random sample of 225 subjects, the sample proportion is
found to be pˆ 0.51.
(a) Determine the test statistic. Show all work; writing the
correct test statistic, without supporting work, will receive no credit.
(b) Determine the p-value for this test. Show all work; writing
the correct P-value, without supporting work, will receive no credit.
(c) Is there sufficient evidence to justify the rejection
of H0 at the a=0.01 Explain.
22. Consumption of a large amount of alcohol is known to
increase reaction time. To investigate the effects of small amounts of alcohol,
reaction time was recorded for five individuals before and after 2 ounces of
alcohol was consumed by each. Does the data below suggest that the consumption
of 2 ounces of alcohol increases mean reaction time?
Assume we want to use a 0.01 significance level to test the
claim.
·
(a)
Identify the null hypothesis and the alternative hypothesis.
·
(b)
Determine the test statistic. Show all work; writing the correct
test statistic, without
supporting work, will receive no credit.
·
(c)
Determine the p-value. Show all work; writing the correct
critical value, without
supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that
the consumption of 2 ounces of alcohol increases mean reaction time? Justify
your conclusion.
23. A STAT 200 instructor is interested in whether there is any
variation in the final exam grades between her two classes Data collected from
the two classes are as follows:
Her null hypothesis and alternative hypothesis are:
1. Determine the test statistic. Show all
work; writing the correct test statistic, without supporting work, will receive
no credit.
b. Determine the p-value for this test. Show
all work; writing the correct P-value, without supporting work, will receive no
credit.
(c) Is there sufficient evidence to justify the rejection
of H0 at the 0.01 Explain.
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