Download Math 112 Final Exam Fall 2006

Name (Print)____________________________
Math 112 Elementary Statistics Fall 2006
Final Exam
150 Points Total
Good Luck!
Directions:
 Whenever possible draw and shade corresponding area!
 Must show logical work for full credit!
 Box answers when possible!
I. Define the following terms: (2 points each, roman numeral I - IV)
1. Sample:
__________________________________________________________________
___________________________________________________________
2. Population:
__________________________________________________________________
_______________________________________________________
3. Standard Deviation: _________________________________________________
__________________________________________________________________
4. Parameter:
_________________________________________________________
__________________________________________________________________
5. Random Sample:
____________________________________________________
__________________________________________________________________
6. Statistic (This is not the word statistics!)_________________________________
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Name (Print)____________________________
II.
Give an example of the following types of data:
a. Discrete Data:
b. Continuous Data:
c. What kind of data is “a” or “b” Quantitative or Qualitative
d.
III.
Give an example of Qualitative data:
True or False
a. The probability of an impossible event is 0.
T
or
F
b. The probability of an event that is certain is 1. 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.
F-distribution is used to compare variances between two samples. T or F
i. The normal distribution is a continuous distribution. T
j.
IV.
or F
Standard normal distribution has a mean 0 and standard deviation 1. T or F
Name the unbiased estimators that target the population parameter.
1. _______________
2. ________________
3. ________________
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Name (Print)____________________________
V. Construct a relative frequency table and histogram for the given frequency
distribution. Draw the graph neatly; label the horizontal axis and vertical axis. (12
points)
Incomes
200-300
301-400
401-500
501-600
>600
Frequency
69
73
81
65
16
VI. For a large data set of average student grades, the third quartile Q3 is found to be
78.5. What does this mean when we say that 78.5 is the third quartile? (6 points)
VII. What is the difference between a standard normal distribution and a nonstandard
normal distribution? (6 points)
VIII. Assume that X has a normal distribution, find the indicated probability. (12 points)
“mu” is 137, “sigma” = 5.3
Find the probability that X is between 134.4 and 140.1
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Name (Print)____________________________
IX.
Assume man’s highs are normally distributed with  = 63.6 in and  = 2.5 in.
(14 points)
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.
X.
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. (12 points)
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Name (Print)____________________________
XI.
The weights of 19 boxes of cereal are measured. The sample standard deviation
is 0.18 ounces. The sample mean is 14.91 oz. We are concerned that the mean
weight of all boxes may be under 15 oz. ( 14 points)
a. State the null and alternative hypothesis.
b. Test the null hypothesis at the 5% level, using either p-value or classical
approach, showing calculation of the test statistic. Word final conclusion
in terms of original claim.
XII.
Each person in a group of 300 students was identified as male or female and
then asked whether he or she preferred taking liberal arts courses in the area or
math-science, social science, or humanities. The table below shows the
frequency found in these categories. Does the sample present sufficient
evidence to reject the null hypothesis: “Preference for math-science, social
science, or humanities is independent of the gender of a college student?
Complete the hypothesis test using the 0.05 level of significance. (12 points)
Gender
Male
Female
Total
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Math-Science
37
35
Social Science
41
72
Humanities
44
71
Total
Name (Print)____________________________
XIII.
Twenty-five newspapers readers were asked how much time, estimated to the
nearest minute they spend reading yesterday’s newspaper. Their times are
listed by the age category of the reader. (15 points)
-AgeX= time
spent
reading
newspaper
yesterday
18-24
10
5
15
4
25-29
13
8
20
10
30-34
14
7
20
35-49
20
12
5
28
15
50-64
20
12
18
15
30
65 and up
8
30
35
20
Use the one way ANOVA technique to test the claim that a person’s age has an effect on
the average amount of time spent daily reading the newspaper? Use alpha 0.05.
a. Set up the null and alternative hypothesis.
b. Display calculator results in the ANOVA table below
Source
Sum or
Squares
(SS)
Degrees of
Freedom
(df)
Mean
Square
Error (MS)
F
P-value
Treatment
Error
Total
c. Test the hypothesis and word final conclusion in terms of original claim.
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