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Test Review for Data Analysis Test
I.
Name : _________________________
Multiple Choice. Choose the one best answer.
1. In a large population of adults, the mean IQ is 115 with a standard deviation of
15. Suppose 100 adults are randomly selected for a market research
campaign. The distribution of the sample mean IQ is
A)
exactly normal, mean 115, standard deviation 20.
B)
approximately normal, mean 115, standard deviation 0.1.
C)
approximately normal, mean 115, standard deviation 1.5.
D)
approximately normal, mean 115, standard deviation 20.
E)
exactly normal, mean 115, standard deviation 1.5.
2. The central limit theorem is important because it allows us to use the Normal
distribution to make inferences about the population mean
A) if the sample size is reasonably large
B) if the population is Normally distributed and the sample size is reasonably
large
C) if the population is Normally distributed
D) if the population is Normally distributed and the population variance is known
E) if the population size is reasonably large
3. A 90% confidence interval for the mean math scores for a population of fifth-graders
is (43.6, 58.9). If you computed a 95% confidence interval using the same
information, which of the following statements is correct?
A) The intervals have the same width.
B) The 95% confidence interval is wider.
C) The 95% confidence interval is shorter.
D) The margin of error can’t be found.
E) The answer can’t be determined from the information given.
4.
What is the margin of error of the mean of 100 data items with a standard deviation
of 2.3 and a mean of 84.1 ? Use a confidence level of 95%
A) 0.045
B) 0.451
C) 79.895
D) 81.8
E) Cannot be determined with information given
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5. If all other parts of problem stay the same, which of the following would reduce the
width of a confidence interval for a given population.
I.
Increase the sample size.
II.
Have a smaller sample standard deviation.
III.
Increase the confidence level.
A)
B)
C)
D)
E)
II.
I only
II only
III only
I and II only
I, II, and III
Free Response questions. Answer completely, but be precise.
6. Consider the sampling distribution of sample means obtained by random sampling from
an infinite population. This population has a distribution that is highly skewed toward the
larger values.
a. How is the mean of the sampling distribution related to the mean of the population?
b. How is the standard deviation of the sampling distribution related to the standard
deviation of the population?
c. How is the shape of the sampling distribution affected by the sample size?
7. A random sample of 100 households in a certain affluent community yields a
mean weekly food budget of $100 and a standard deviation of $10. Find the 95%
confidence interval for weekly food budgets of households in this community.
8. What is the margin of error of the mean of 80 data items with a standard
deviation of 0.96 and a mean of 51.2 ? Use a confidence level of 90 %
2
9. Determine the confidence interval of the population mean for a set of 100 data with
a standard deviation of 3 and sample mean of 116. Use 99% confidence level.
Do the same problem with 95% and 90 % confidence level and analyze the data
based on the confidence interval.
10. Determine the confidence interval of the population mean of a sample of 50
items with a sample mean 14.5, standard deviation 2.8 at a confidence level
of 95%
11. Ten samples are collected, each containing 30 items. The means of the
samples are 29, 38, 45, 26, 37, 32, 28, 30, 28, 40. What is the mean of the
sample means ?
12. In a random survey of 100 high school students in Georgia it has been found
that the number of students who study more than 20 hours per week were
22. What is the population proportion of students who study more than 20
hours in Georgia and what is the population standard deviation for the above
data?
13. It has been found in a survey that the mean of the sampling distribution for
the number of hours students spend time watching TV per day is 3 hours
with a population standard deviation of .25. What is the population mean?
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Formulas for the Data
Analysis Unit
X  
p̂  p

X 
n
p(1  p)
 p̂ 
n
np  10,
n(1  p)  10
xz
*
p̂  z *
Level of
Confidence
z*

n
p(1  p)
n
90%
1.645
95%
1.96
4
99%
2.576