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STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Question
(b) If the variance of a data set is 0, then all the observations in
this data set must be zero.
(c) If a 95% confidence interval for a population mean contains 1, then
the 99% confidence interval for the same parameter must contain 1
(d) When plotted on the same graph, a distribution with a mean of 60 and
a standard deviation of 5 will look more spread out than a distribution with a
mean of 40 and standard deviation of 8.
(e) In a two-tailed test, the value of a test statistic is 2. The test
statistic follows a distribution with the distribution curve shown below. If we know the
shaded area is 0.03, then we have sufficient evidence to reject the null
hypothesis at 0.05 level of significance.
.jpg">.jpg">
(a) A study was conducted at a local college to analyze the average GPA
of students graduated from UMUC in 2015. 100 students graduated from UMUC in 2015 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) A STAT 200 student is interested in the number of credit cards owned
by college students. She surveyed all of her classmates to collect sample data. This type of
sampling is called:
(i) simple random
(ii) convenience
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 3 of 8
(iii) systematic
(iv) stratified
(a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10
programs had 50 subjects in it. The subjects were followed for 12 months. Weight change
for each subject was recorded. You want to test the claim that the mean weight loss is the same for the
10 programs.What
statistical approach should be used?
(i) t-test
(ii) linear regression
(iii) ANOVA
(iv) confidence interval
(b) A STAT 200 instructor teaches two classes. She wants to
test if the variances of the score distribution for the two classes are
different. What type of
hypothesis test should she use?
(i) t-test for two independent samples
(ii) t-test for matched samples
(iii) z-test for two samples
(iv) F- test
4. The frequency distribution below shows the distribution for IQ scores
for a random sample of 1000 adults. (Show all work. Just the answer, without supporting
work, will receive no credit.)
.jpg">.jpg">|
IQ
Scores
|
Frequency
|
Relative
Frequency
|
||
|
50
|
- 69
|
23
|
||
|
70
|
- 89
|
0.250
|
||
|
90 -109
|
450
|
|||
|
110
|
- 129
|
|||
|
130
|
- 149
|
23
|
||
|
Total
|
1000
|
|||
.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">
(a) Complete the frequency table with frequency and relative frequency. Express the
relative frequency to three decimal places.
(b) What percentage of the adults in this sample has an IQ score of at
least 110?
(c) Does this distribution have positive skew or negative skew? Why or
why not?
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 4 of 8
.jpg">
5. The five-number summary below shows the grade distribution of a STAT 200
quiz for a sample of 800 students.
.jpg">
(a) What is the range in the grade distribution?
(b) Which score band has the fewest students?
(i) 30 - 60
(ii) 60 - 85
(iii) 80 - 100
(Iv) Cannot be determined
(c) How many students are in the score band between 70 and 85?
6. Consider selecting one card at a time from a 52-card deck. What is the
probability that the first card is from the suit of hearts and the second card
is also from the suit of hearts? (Note: There are 13 cards from the suit of hearts
in a deck of cards) (Show
all work. Just the answer,
withoutsupporting work, will receive no credit.)
(a) Assuming the card selection is without replacement.
(b) Assuming the card selection is with replacement.
7. There are 1000 students in a high school. Among the 1000
students, 250 students take AP Statistics, and 100 students take AP French. 80 students
take both AP courses. Let S be the event that a randomly selected student takes AP Statistics,
and F be the event that a randomly selected student takes AP French. 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 F).
(b) What is the probability of complement event of (S OR F)?
.jpg">.jpg">
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 5 of 8
.jpg">
8. Consider rolling a fair 6-faced die twice. Let A be the
event that the sum of the two rolls is at least 10, and B be the event that the
first one is a multiple of 3.
(a) What is the probability that the sum of the two rolls is at least 10
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.
9. There are 5 books in the“ Statistics isFun” series. (Show all work. Just the answer, without supporting work, will receive no credit).
(a) How many different ways can Mimi arrange the 5 books in her book
shelf?
(b) Mimi plans on bringing two of the five books with her in a road trip. How many
different ways can the two books be selected?
.jpg">.jpg">|
10.
|
|||||||
|
supporting work, will receive no credit.
|
|||||||
|
x
|
-2
|
-1
|
0
|
1
|
2
|
||
|
P(x)
|
0.1
|
0.1
|
0.3
|
0.2
|
0.3
|
||
.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">
11. Mimi joined UMUC basketball team since summer 2016. On average, she
is able to score 30% of the field goals. Assume she tries 15 field goals in a game.
(a) Let X be the number of field goals that Mimi scores in the game. 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 Mimi scores at least 2 of the 15 field
goals. (round the
answer to 3 decimal places) Show
all work. Just the answer,
without supporting work, will receive no credit.
12. A research concludes that the number of hours of exercise per week for
adults is normally distributed with a mean of 3.5 hours and a
standard deviation of 3 hours. Show
all work. Just the answer,
without supporting work, will receive no credit.
(a) Find the 80th percentile for the distribution of exercise time
per week. (round the
answer to 2 decimal places)
(b) What is the probability that a randomly selected adult has more than
7 hours of exercise per week? (round the answer to 4 decimal places)
13. Assume the SAT Mathematics Level 2 test scores are normally distributed
with a mean of 500 and a standard deviation of 100. Show all work.Just the answer, without supporting
work, will receive no credit.
.jpg">.jpg">
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 6 of 8
(a) Consider all random samples of 64 test scores. What is the
standard deviation of the sample means?
(b) What is the probability that 64 randomly selected test scores will
have a mean test score that is between 475 and 525?
14. An insurance company checks police records on 1200 randomly selected
auto accidents and notes that teenagers were at the wheel in 180 of them. Construct a 90%
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.
15. A city built a new parking garage in a business district. For a random
sample of 64 days, daily fees collected averaged $2,000, with a standard
deviation of $400. Construct a 95% confidence interval estimate of the mean daily income
this parking garage generates. Show
all work. Just the
answer, without supporting work, will receive no credit.
16. ABC Company claims that the proportion of its employees investing in
individual investment accounts is higher than national proportion of 45%.A survey of
100 employees in ABC Company indicated that 50 of them have invested in an individual
investment account. 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 ABC Company’ s claim that
the proportion of its employees investing in individual investment accounts is
higher than 45%? Explain.
17. Mimi was curious if regular excise really helps weight loss, hence she
decided to perform a hypothesis test. A random sample of 5 UMUC students was chosen. The students
took a 30-minute exercise every day for 6 months. The weight was
recorded for each individual before and after the exercise regimen. Does the data
below suggest that regular exercise helps weight loss?
.jpg">.jpg">.jpg">.jpg">.jpg">|
Weight
(pounds)
|
||
|
Subject
|
Before
|
After
|
|
1
|
160
|
130
|
|
2
|
170
|
160
|
|
3
|
185
|
175
|
|
4
|
165
|
165
|
|
5
|
200
|
190
|
.jpg">
(a) Identify the null hypothesis and the alternative hypothesis.
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 7 of 8
(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 evident to support the claim that regular
exercise helps weight loss? Justify your conclusion.
18. In a pulse rate research, a simple random sample of 50 men results in a
mean of 80 beats per minute, and a standard deviation of 11.5 beats per
minute. Based on the
sample results, the researcher concludes that the pulse rates of men have a
standard deviation greater than 10 beats per minutes. Use a 0.10
significance level to test the researcher’ s claim.
.jpg">|
(a)
|
Identify
the null hypothesis and alternative hypothesis.
|
|||||||||||
|
(b)
|
||||||||||||
|
supporting work, will receive no credit.
|
||||||||||||
|
(c)
|
||||||||||||
|
supporting work, will receive no credit.
|
||||||||||||
|
(d)
|
Is
there sufficient evidence to support the researcher’ s claim? Explain.
|
|||||||||||
|
19.
|
||||||||||||
|
that
the five types are equally popular.Suppose that a sample of 500 purchases yields observed
|
||||||||||||
|
answer.
|
||||||||||||
|
Type
|
1
|
2
|
3
|
4
|
5
|
|||||||
|
Number
of Bags
|
120
|
85
|
110
|
90
|
95
|
|||||||
|
(a)
|
Identify
the null hypothesis and the alternative hypothesis.
|
|||||||||||
|
(b)
|
||||||||||||
|
(c)
|
supporting work, will receive no credit.
|
|||||||||||
|
(d)
|
work, will receive no credit.
|
|||||||||||
|
Is
there sufficient evidence to support themanager’s claim that the five types
of candy
|
||||||||||||
|
bags
are equally popular? Justify your answer.
|
||||||||||||
.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">
STAT 200: Introduction to Statistics Final Examination, Fall 2016 OL3
Page 8 of 8
20. A STAT 200
instructor believes that the average quiz score is a good predictor of final
examscore. A random sample
of 10 students produced the following data where x is the average quiz score
and y is the final exam score.
.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">.jpg">|
x
|
80
|
50
|
60
|
100
|
70
|
85
|
40
|
65
|
75
|
80
|
|
y
|
72
|
75
|
65
|
90
|
60
|
85
|
50
|
60
|
75
|
90
|
(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 scor
|
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