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Name (Print)____________________________
Math 112 Elementary Statistics Spring 2009
Final Exam
150 Points Total
Good Luck!
I. Define the following terms: (2 points each)
1. Sample:
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2. Population:
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3. Standard Deviation:
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4. Parameter:
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5. Random Sample:
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6. Statistic (This is not the word statistics!)
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II.
Give an example of the following types of data:
a. Discrete Data:
b. Continuous Data:
c.
III.
Give an example of Qualitative data:
True or False
a. The probability of an impossible event is 1.
T
or
F
b. The probability of an event that is certain is 0. T
or
F
c. Probability can be negative on rare occasions.
or
T
F
d. Two events are independent if the occurrence of one does not affect the
probability of the occurrence of the other.
T or F
e. For a data set that has a distribution that is approximately bell shape about
95% of all values lie with 2 standard deviation from the mean. T or F
f. Student t-distribution is used to test claim about the mean when sigma is
known. T or F
g. Chi square is used to test claim about standard deviation or variance T or F
h. The normal distribution is a discrete distribution. T
i.
or F
Standard normal distribution has a mean 1 and standard deviation 1. T or F
j. Pr(at least one)=1-Pr(none) T or F
k. Binomial distribution is a continuous distribution T or F
l. Sample data from two different populations are used to construct this 95%
CI : 0.20 < p1-p2 < 0.30. There is evidence the two populations are the
equal. T or F
IV.
Name the unbiased estimators that target the population parameter.
1. _______________
2. ________________
3. ________________
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V. For a large data set of student grades, the first quartile Q1 is found to be 73.4. What
does this mean when we say that 73.4 is the first quartile? (8 points)
VI. Assume that X has a normal distribution, find the indicated probability. (10 points)
The mean is 15.2 and standard deviation is 0.9. Find the probability that X is between
15.2 and 16. Graph.
VII. Assume man’s highs are normally distributed with  = 63.6 in and  = 2.5 in.
( 12 points total)
a.
If a man is randomly selected find the probability that his height is between
63.5in and 64.5 in.


b. If 16 man are normally selected, find the probability that they have a mean height
between 63.5 in and 64.5 in.
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VIII. In a sample of 70 students, 42 plan to graduate next year. Find the 95% confidence
interval for the percentage of students planning to graduate next year. (10 points)
IX.
A bank’s loan officer rates applicants for credit. The ratings are normally
distributed with a mean of 200 and a standard deviation of 50. Find the top 5%
credit rating, which separates the bottom 95% from the top 5%. (10 points)
X.
In a clinical test of the drug “ Statistics” 17.8% of the subjects treated
experience headaches. Six subjects are randomly selected. Find the probability
that at least one subjects experience headaches. Show formula and work! (10
points)
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Name (Print)____________________________
XI.
Find the mean, median, mode, variance and standard deviation of the following
sample { 2, 3, 1, 9} Must show logical work step by step for full credit ! ( 10
points)
XII.
Find the mean and standard deviation. Let the random variable x represent the
number of tails when you toss a fair coin two times. Construct a table describing
a probability distribution, check, find mean and standard deviation. ( 10 points)
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XIII. Claim: The mean life span of desktop PCs is less than 5 years.
Data: n=21, sample mean=6.9years, s=2.4 years. Alpha=0.05
(10 points) Answer the following:
1) Set up Ho, Ha. 2) Find test statistic. 3) Graph and shade appropriate region.
4) Test your claim, decision and why. 5) Interpret.
IX. Find the value of the linear correlation coefficient r and test for significant at a 0.05
level. Then construct a regression equation and predict for the Math score for a Reading
score of 40. (10 points)
Reading (x)
40
36
42
29
44
35
38
42
45
Math (y)
78
80
90
60
95
70
77
83
90
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