Download Sample Final Exam

BASIC STATISTICS ECOE 1323
SPRING 2006
FINAL EXAM
NAME:___________________________________________ ID NUMBER:______________
INSTRUCTIONS:
1. Write your name and student ID.
2. You have 2 hours
3. This exam must be your own work entirely. You cannot talk to or share information
with anyone.
4. Show all your work. Partial credit will only be given where sufficient understanding
of the problem has been demonstrated and work is shown.
QUESTION
POINTS
DON'T WRITE ON THIS TABLE
#1
#2
#3
1
TOTAL
SECTION 1: MULTIPLE-CHOICE
For each question in this section, circle the correct answer. (Problem is worth 2 pts.)
Questions 1-2 refer to the following information:
1- The height of Palestinian men aged 18 to 24 are approximately normally distribution with
mean 68 inches and standard deviation 2.5 inches. Half of all young men are shorter than
a) 65.5 inches
b) 68 inches
c) 70.5 inches
d) Can't tell, because the median height is not given.
2- Only about 5% of young men have heights outside the range
a)
b)
c)
d)
65.5 inches to 70.5 inches
63 inches to 73 inches
60.5 inches to 75.5 inches
58 inches to 78 inches
Questions 3-4 refer to the following information:
3- A copy machine dealer has on the number x of copy machines at each of 89 customer
locations and the number y of service calls in a month at each location. Summary
calculations give x  8.4, s x  2.1, y 14.2, s y  3.8, and r  0.86 . What is the slop of the
least squares regression line of number of service calls on number of copiers?
a)
b)
c)
d)
e)
0.86
1.56
0.48
Non of these
Can't tell from the information given
4- About what percent of the variation in number of service calls is explained by the linear
relation between number of service calls and the number of machines?
a)
b)
c)
d)
e)
86%
93%
74%
Non of these
Can’t tell from the information given
5- In a study of the effects of acid rain, random sample of 100 trees from a particular forest are
examined. Forty percent of these show some signs of damage. Which of the following statements
are correct?
a) 40 % is a parameter
b) 40 % is a statistic
c) 40 % of all trees in this forest show some signs of damage
d) more than 40 % of the trees in this forest show some signs of damage
e) less than 40 % of the trees in this forest show some signs of damage
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6- You play tennis regularly with a friend and from past experience you believe that the outcome of
each match is independent. For any given match you have a probability of 0.6 of winning. The
probability that you win the next tow matches is
a) 0.36
b) 0.6
c) 0.4
d) 0.16
e) 1.2
Questions 6-7 refer to the following information:
6- In a large population of college students, 20 % of the students have experienced feelings of math
anxiety. If you take a random sample of 10 students from this population, the probability that
exactly 2 students have experienced math anxiety is
a) 0.3020
b) 0.2634
c) 0.2013
d) 0.5
e) 1
7- The standard deviation of the sample proportion of students who have experienced math anxiety
is
a) 0.0160
b) 0.1265
c) 0.2530
d) 1
e) 0.2070
8- You want to estimate the mean SAT score for a population of students with a 90% confidence
interval. Assume that the population standard deviation is  = 100. if you want the margin of error
of the to be approximately 5, you will need a sample size of
a) 33
b) 1083
c) 11
d) 1476
e) non of the above
Questions 9-10 refer to the following information:
20- A 95% confidence interval for the mean reading achievement score for a population of third
grades is (44.2 , 54.2). The margin of error of this interval is
a) 95%
b) 5
c) 2.5
d) 54.2
e) The answer cannot be determined from the information given
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10- The sample mean is
a) 44.2
b) 54.2
c) 0.95
d) 49.2
e) The answer cannot be determined from the information given
11- Using the same set of data, you compute a 95% confidence interval and a 99% confidence
interval. Which of the following statement is correct?
a) The intervals have the same width
b) The 99% interval is wider
c) The 95 % interval is wider
d) You cannot be determined which interval is wider unless you know n and s.
12. You have measured the systolic blood pressure of a random sample of 25 employees of a
company. A 95% confidence interval for the mean systolic blood pressure for the employees is
computed to be (122,138). Which of the following statements gives a valid interpretation of this
interval?
(a) About 95% of the samples of employees have a systolic blood pressure between 122 and
138.
(b) About 95% of the employees in the company have a systolic blood pressure between 122
and 138.
(c) If the sampling procedure were repeated many times, then approximately 95% of the
resulting confidence intervals would contain the mean systolic blood pressure for
employees in the company.
(d) If the sampling procedure were repeated many times, then approximately 95% of the
sample means would be between 122 and 138.
13. Popular wisdom is that eating pre-sweetened cereal tends to increase the number of dental caries
(cavities) in children. A sample of children was (with parental consent) entered into a study and
followed for several years. Each child was classified as a sweetened-cereal lover or a nonsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here is
the summary data:
Sugar Bombed No sugar
Sample size
10
15
Sample mean
6.41
5.20
Sample standard deviation
5.0
15.0
A 95% confidence interval for the means difference assuming unequal variances is
(a)
6.41  5.20  2.262
(b)
6.41  5.20   2.262
5 15

10 15
25 225

10 15
(c) 6.41  5.20  1.96 25  225
10
15
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(d)
6.41  5.20  2.06912.11
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1

10 15
14. Wages for a particular industry are normally distributed with an average of $11.90 an hour and a
standard deviation of $0.40. What percentage of workers receive between $10.90 and $12.90
(a) 0.9938
(b) 0.0062
(c) 0.9876
(d) 0.0124
15. The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC)
are normally distributed with mean, µ = 100, and standard deviation, =15. What score must a
child achieve on the WISC in order to fall in the top 6.3% of the population?
(a) 77.05
(b) ­77.05
(c) 129.4
(d) 122.95
16. A nationwide test has a mean of 75 and a standard deviation of 10. A random sample of 64
examinees was drawn and their scores were recorded. The probability that the sample mean is
greater than 78 is
(a) 0.0082
(b) 0.4918
(c) 0.1179
(d) 0.3821
17. An airplane is only allowed a gross passenger weight of 8000 kg. If the weights of passengers
traveling by air between Toronto and Vancouver have a mean of 78 kg and a standard deviation
of 7 kg, the approximate probability that the combined weight of 100 passengers will exceed
8,000 kg is:
(a) 0.4978
(b) 0.3987
(c) 0.0044
(d) 0.0022
18. In order to estimate the average time spent on the computer terminals per student at a local
university, data were collected from a sample of 81 business students over a one-week period.
Assume the population standard deviation is 1.2 hours. For a 95% confidence interval, the
margin of error for estimating the population mean is
(a) 0.26
(b) 1.96
(c) 0.03
(d) 0.21
19. A researcher wants to estimate the difference between the average response times (in minutes)
of emergency 911 telephone calls for two cities. Based on a simple random sample of 75 calls from
each city last month, the sample averages were 13 minutes for City 1 and 9 minutes for City 2. The
sample standard deviations were 2.1 minutes for City 1 and 1.7 minutes for City 2.
A 90% confidence interval for the difference between the two population mean response times is
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(a)
(b)
(c)
(d)
(3.38, 4.62)
(3.55, 4.45)
(3.49, 4.51)
(3.62, 4.60)
20. Which of the following statements about confidence intervals is INCORRECT?
(a) If we keep the sample size fixed, the confidence interval gets wider as we increase the
confidence coefficient.
(b) A confidence interval for a mean always contains the sample mean.
(c) If we keep the confidence coefficient fixed, the confidence interval gets narrower as we
increase the sample size.
(d) If the population standard deviation increases, the confidence interval decreases in
width.
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SECTION 1: FREE RESPONSE QUESTIONS
Question #1
A company wanted to know if attending a course on "how to be a successful salesperson" can
increase the average sales of its employees. The company sent six of its salespersons to attend this
course. The following table gives the week sales of these salespersons before and after they
attended this course.
Before 12 18 25 9 14 16
After 18 24 24 14 19 20
Using the 1% significance level, can you conclude that the mean weekly sales for all salespersons
increase as a result of attending this course? Assume that the population of paired difference has a
normal distribution.
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Question (2)
A political analyst was curious if younger adults were becoming more conservative. He decided
to see if the mean age of registered Republicans was lower than that of registered Democrats. He
selected an SRS of 128 registered Republicans from a list of registered Republicans and
determined the mean age to be x 1  39 years, with a standard deviation S 1  8 years. He also
selected an independent SRS of 200 registered Democrats from a list of registered Democrats and
determined the mean age to be x 2  40 years, with a standard deviation S 1  10 years. Let
1 and 2 represent the mean ages of the populations of all registered Republicans and
Democrats, respectively. Suppose that the distributions of age in the populations of registered
Republicans and of registered Democrats have the same standard deviation. Assume the pooled
two-sample t-procedures are safe to use.
a. Construct and 90% confidence interval for 1 -2 . Interpret your finding.
b. State H0 and Ha.

Ho:

Ha:
c. Calculate the test statistic.
d. Compute the P-value.
e. State your conclusion at level of significance   .05 .
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