1. True or False. Justify for full credit.
(a) If all the observations in a data set are identical, then the variance for this data set is zero.
(b) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.
(c) The mean is always equal to the median for a normal distribution.
(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.
(e) It’s easier to reject the null hypothesis in a hypothesis test at 0.05 significance level than at 0.01
significance level.
2. Choose the best answer. Justify for full credit.
(a) A study was conducted at a local college to analyze the average GPA of students graduated from
UMUC in 2016. 100 students graduated from UMUC in 2016 were randomly selected, and the average
GPA for the group is 3.5. The value 3.5 is a
(i) statistic (ii) parameter (iii) cannot be determined
(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is
(i) interval (ii) nominal (iii) ordinal (iv) ratio
(c) On the day of the Virginia Primary Election, UMUC News Club organized an exit poll at three polling
stations were randomly selected and all voters were surveyed as they left those polling stations. This
type of sampling is called:
(i) cluster (ii) convenience (iii) systematic (iv) stratified 3. A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency
distribution below shows the distribution for study time each week (in hours). (Show all work. Just the
answer, without supporting work, will receive no credit.)
Study Time (in hours)
0.0 – 4.9
5.0 - 9.9
10.0 – 14.9
15.0 – 19.9
20.0 – 24.9
total Frequency
2
13
20 Relative Frequency 0.45
100 (a) Complete the frequency table with frequency and relative frequency. Express the relative frequency
to two decimal places.
(b) What percentage of the study times was at least 15 hours?
(c)
In what class interval must the median lie? 5.0 – 9.9, 10.0 -14.9, 15.0 – 19.9, or 20.0 – 24.9?
Why? 4. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 60
students.
Answer each question based on the given information, and explain your answer in each case.
(a) What is the range in the grade distribution?
(b) Which of the following score bands has the most students?
(i) 30 – 50
(ii) 50 - 70
(iii) 85 – 100
(Iv) Cannot be determined
(c) How many students in the sample are in the score band between 65 and 100?
5. A basket contains 3 white balls, 2 yellow balls, and 5 red balls. Consider selecting one ball at a time
from the basket. (Show all work. Just the answer, without supporting work, will receive no credit.)
(a) Assuming the ball selection is with replacement. What is the probability that the first ball is white and
the second ball is also white?
(b) Assuming the ball selection is without replacement. What is the probability that the first ball is yellow
and the second ball is red?
6. There are 1000 juniors in a college. Among the 1000 juniors, 300 students are taking STAT200, and
150 students are taking PSYC300. There are 100 students taking both courses. Let S be the event that a
randomly selected student takes STAT200, and P be the event that a randomly selected student takes
PSYC300. (Show all work. Just the answer, without supporting work, will receive no credit.)
(a) Provide a written description of the complement event of (S OR P).
(b) What is the probability of complement event of (S OR P)?
7. Consider rolling a fair 6-faced die twice. Let A be the event that the product of the two rolls is at most
5, and B be the event that the first one is a multiple of 3.
(a) What is the probability that the product of the two rolls is at most 5 given that the first one is a
multiple of 3? Show all work. Just the answer, without supporting work, will receive no credit.
(b) Are event A and event B independent? Explain.
8. Answer the following two questions. (Show all work. Just the answer, without supporting work, will
receive no credit).
(a) A bike courier needs to make deliveries at 6 different locations. How many different routes can he
take?
(b) Mimi has eight books from the Statistics is Fun series. She plans on bringing three of the eight books
with her in a road trip. How many different ways can the three books be selected? 9. Let random variable x represent the number of heads when a fair coin is tossed three times.
(a) Construct a table describing the probability distribution.
(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)
10. 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.
(a) Let X be the number of the serves that Mimi returns. 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. (round the
answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no
credit.
11. The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation
of 2 feet. Show all work. Just the answer, without supporting work, will receive no credit.
(a) What is the probability that a randomly selected pecan tree is between 7 and 11 feet tall? (round
the answer to 4 decimal places)
(b) Find the 40th percentile of the pecan tree height distribution.
(round the answer to 2 decimal places)
12. Based on the performance of all individuals who tested between July 1, 2012 and June 30, 2015, the
GRE Quantitative Reasoning scores are normally distributed with a mean of 152.47 and a standard
deviation of 8.93. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work. Just the
answer, without supporting work, will receive no credit. (a) Consider all random samples of 49 test
scores. What is the standard deviation of the sample means? (Round your answer to three decimal
places) (b) What is the probability that 49 randomly selected test scores will have a mean test score that
is greater than 150? (Round your answer to four decimal places)
13. An insurance company checks police records on 600 randomly selected auto accidents and notes that
teenagers were at the wheel in 90 of them. Construct a 95% confidence interval estimate of the
proportion of auto accidents that involve teenage drivers. Show all work. Just the answer, without
supporting work, will receive no credit.
14. In a study designed to test the effectiveness of acupuncture for treating migraine, 100 patients were
randomly selected and treated with acupuncture. After one-month treatment, the number of migraine
attacks for the group had a mean of 2 and standard deviation of 1.5. Construct a 95% confidence interval
estimate of the mean number of migraine attacks for people treated with acupuncture. Show all work.
Just the answer, without supporting work, will receive no credit.
15. Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the
adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample chose
banana as his / her favorite fruit.
Assume Mimi wants to use a 0.10 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 for this test. Show all work; writing the correct P-value, without supporting
work, will receive no credit.
(d) Is there sufficient evidence to support the claim that banana is the favorite fruit for more than 50% of
the adults.? Explain.
16. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each
was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The
result is shown in the following table.
Subject
1
2
3
4
5 1 hour later
14
18
11
13
12 Numbers of words recalled
24 hours later
12
15
9
12
12 Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean
recall after 24 hours? Assume we want to use a 0.05 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 P-value, without supporting work, will
receive no credit.
(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1
hour exceeds the mean recall after 24 hours? Justify your conclusion.
17. In a pulse rate research, a simple random sample of 600 men results in a mean of 80 beats per
minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the researcher
concludes that the pulse rates of men have a standard deviation less than 12 beats per minutes. Use a
0.05 significance level to test the researcher’s claim.
(a) Identify the null hypothesis and 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 for this test. Show all work; writing the correct P-value, without supporting
work, will receive no credit.
(d) Is there sufficient evidence to support the researcher’s claim? Explain. 18. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four
types are equally popular. Suppose that a sample of 500 purchases yields observed counts of 150, 125,
105, and 120 for types 1, 2, 3, and 4, respectively.
type
number 1
150 2
125 3
105 4
120 Assume we want to use a 0.05 significance level to test the claim that the four types are equally popular.
(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 P- value, without supporting work, will
receive no credit.
(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular?
Justify your answer.
19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A
random sample of 10 students produced the following data where x is the average quiz score and y is the
final exam score.
X
Y 80
70 93
96 50
50 60
70 100
96 40
38 85
83 70
65 75
77 85
87 (a) Find an equation of the least squares regression line. Show all work; writing the correct equation,
without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted final exam score if the average quiz score
is 90? Show all work and justify your answer.
20. A study of 10 different weight loss programs involved 200 subjects. Each of the 10 programs had 20
subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded.
We want to test the claim that the mean weight loss is the same for the 10 programs.
Source of variation Sum of squares (ss) Factor (between)
Error (within)
total 65.4
653.05 Degrees of freedom
(df) Mean square (ms) 199 n/a (a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square
(Show all work):
(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 P-value, without supporting work, will
receive no credit.
(d) Is there sufficient evidence to support the claim that the mean weight loss is the same for the 10
programs at the significance level of 0.05? Explain.

 

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