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COMPREHENSIVE TUTORIAL_III
Estimation: Point and Interval Estimation,
Estimator and Estimates, Confidence Intervals,
Interval Estimates of Mean and Proportion from
Large Samples, Interval Estimation Using t
Distribution, Sample Size for Estimating Means
and Proportions
1. Define a point estimate : Answer : A point
estimate is a single valued estimate of a
population parameter.
2. Define an Esimator & an Estimate: Estimator is a
sample statistics used to estimate population
parameter and Estimate is a specific observed
value of an estimator
3. Define an interval estimate : Answer : An
interval estimate is an interval within which the
population parameter is likely to lie.
4. Define level of confidence : Answer : It is the
probability ( generally .90,.95,.99) that the
interval estimate will cover the true value of the
population of interest
5. Define confidence interval: Answer: It is an
interval estimate obtained by a procedure
satisfying the probability requirement. It is found
by constructing an interval around the point
estimate of the form :
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Point Estimate +/- Multiple ( Estimated
standard deviation of point estimate)
where the multiple is often a normal distribution
percentage point or a
t-distribution percentage point.
6. Give point estimates of population mean (µ ) ,
population standard deviation ( ) and
population proportion ( p )
7. Give formulae for sample size for estimating
means & proportions.
8. when t- distribution is used for interval
estimation. It is used when the population is
normally distributed, population s.d is unknown
& sample size is less than 30.
9. What are the four desirable properties of point
estimates? Describe each.
10. In point estimation
a. data from the population is used to estimate
the population parameter
b. data from the sample is used to estimate the
population parameter
c. data from the sample is used to estimate the
sample statistic
d. the mean of the population equals the mean of
the sample
Answer: b
11. The sample statistic s is the point estimator of
a. 
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b. 
c. x
d. p
Answer: b
12. The sample mean is the point estimator of
a. 
b. 
c. x
d. p
Answer: a
13. A sample statistic is an unbiased estimator of
the population parameter if
a. the expected value of the sample statistic is
equal to zero
b. the expected value of the sample statistic is
equal to one
c. the expected value of the sample statistic is
equal to the population parameter
d. it is equal to zero
Answer: c
14. A property of a point estimator that occurs
whenever larger sample sizes tend to provide
point estimates closer to the population
parameter is known as
a. efficiency
b. unbiased sampling
c. consistency
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d. relative estimation
Answer: c
15. The standard deviation of a point estimator is
called the
a. standard deviation
b. standard error
c. point estimator
d. variance of estimation
Answer: b
16. The sample statistic, such as x , s, or p , that
provides the point estimate of the population
parameter is known as
a. a point estimator
b. a parameter
c. a population parameter
d. a population statistic
Answer: a
17. A simple random sample of 5 observations
from a population containing 400 elements was
taken, and the following values were obtained.
12 18 19 20 21
A point estimate of the mean is
a. 400
b. 18
c. 20
d. 10
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Answer: b
18. Given two unbiased point estimators of the
same population parameter, the point estimator
with the smaller variance is said to have
a. smaller relative efficiency
b. greater relative efficiency
c. smaller consistency
d. larger consistency
Answer: b
19. Whenever the estimation process summarizes
all of the information a sample has about a
population parameter, the point estimator has the
property of
a. relative consistency
b. full consistency
c. sufficiency
d. insufficiency
Answer: c
20. The following data was collected from a
simple random sample of a population.
13 15 14 16 12
The point estimate of the population standard
deviation is
a. 2.500
b. 1.581
c. 2.000
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d. 1.414
Answer: b
21. Four hundred people were asked whether gun
laws should be more stringent. Three hundred
said "yes," and 100 said "no." The point
estimate of the proportion in the population who
will respond "yes" is
a. 300
b. approximately 300
c. 0.75
d. 0.25
Answer: c
22. Starting salaries of a sample of five
management majors along with their genders are
shown below.
Salary
Employee
(in $1,000s) Gender
1
30
F
2
28
M
3
22
F
4
26
F
5
19
M
a. What is the point estimate for the starting
salaries of all management majors?
b. Determine the point estimate for the variance
of the population.
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c. Determine the point estimate for the
proportion of male employees.
Answers:
a. 25 (thousands)
b. 20 (thousands)
c. 0.4
23. In order to determine an interval for the mean
of a population with unknown standard deviation
a sample of 25 items is selected. The mean of
the sample is determined to be 23. The number
of degrees of freedom for reading the t value is
a. 22
b. 23
c. 24
d. 25
Answer: c
24. If we want to provide a 95% confidence
interval for the mean of a population, the
confidence coefficient is
a. 0.485
b. 1.96
c. 0.95
d. 1.645
Answer: c
25. As the number of degrees of freedom for a t
distribution increases, the difference between the
t distribution and the standard normal
distribution
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a. becomes larger
b. becomes smaller
c. stays the same
d. None of these alternatives is correct.
Answer: b
26. For the interval estimation of  when  is
known and the sample is large, the proper
distribution to use is
a. the normal distribution
b. the t distribution with n degrees of freedom
c. the t distribution with n - 1 degrees of freedom
d. the t distribution with n - 2 degrees of freedom
Answer: a
27. An estimate of a population parameter that
provides an interval of values believed to contain
the value of the parameter is known as the
a. confidence level
b. interval estimate
c. parameter value
d. population estimate
Answer: b
28. In developing an interval estimate, if the
population standard deviation is unknown
a. it is impossible to develop an interval estimate
b. the standard deviation is arrived at using
historical data
c. the sample standard deviation can be used
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d. it is assumed that the population standard
deviation is 1
Answer: c
29. When the level of confidence increases, the
confidence interval
a. stays the same
b. becomes wider
c. becomes narrower
d. becomes narrower for small sample sizes
Answer: b
30. A random sample of 144 observations has a
mean of 20, a median of 21, and a mode of 22.
The population standard deviation is known to
equal 4.8. The 95.44% confidence interval for
the population mean is
a. 15.2 to 24.8
b. 19.200 to 20.800
c. 19.216 to 20.784
d. 21.2 to 22.8
Answer: b
31. A random sample of 16 students showed an
average age of 25 years and a standard deviation
of 2 years. The 98% confidence interval for the
true average age of students is
a. 24.329 to 26.67
b. 23.699 to 26.301
c. 24.487 to 25.513
d. 24.316 to 25.684
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Answer: b
32. The sample size needed to provide a margin of
error of 2 or less with a .95 probability when the
population standard deviation equals 11 is
a. 10
b. 11
c. 116
d. 117
Answer: d
33. Which of the following best describes the form
of the sampling distribution of the sample
proportion?
a. When standardized, it is exactly the standard
normal distribution.
b. When standardized, it is the t distribution.
c. It is approximately normal as long as n  30.
d. It is approximately normal as long as np  5
and n(1-p)  5.
Answer: d
34. In a random sample of 144 observations, p =
0.9. The 95% confidence interval for P is
a. 0.851 to 0.949
b. 0.876 to 0.924
c. 0.898 to 0.902
d. 0.1 to 0.9
Answer: a
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35. A random sample of 100 people was taken.
Eighty of the people in the sample favored
Candidate A. The 95% confidence interval for
the true proportion of people who favors
Candidate A is
a. 0.722 to 0.878
b. 0.762 to 0.838
c. 78.04 to 81.96
d. 62.469 to 97.531
Answer: a
36. A machine that produces a major part for an
airplane engine is monitored closely. In the past,
10% of the parts produced would be defective.
With a .95 probability, the sample size that needs
to be taken if the desired margin of error is .05 or
less is
a. 7
b. 33
c. 138
d. 139
Answer: d
37. A sample of 100 cans of coffee showed an
average weight of 13 ounces with a standard
deviation of 0.8 ounces.
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a. Construct a 95% confidence interval for the
mean of the population.
b. Construct a 95.44% confidence interval for the
mean of the population.
c. Discuss why the answers in Parts a and b are
different.
Answers:
a. 12.8432 to 13.1568
b. 12.84 to 13.16
c. As the level of confidence increases, the
confidence interval becomes wider.
38. A random sample of 121 checking accounts
at a bank showed an average daily balance of
$280. The standard deviation is known to be $60.
a. Is it necessary to know anything about the
shape of the distribution of the account
balances in order to make an interval estimate
of the mean of all the account balances?
Explain.
b. Find the standard error of the mean.
c. Give a point estimate of the population mean.
d. Construct 80% and 90% confidence interval
estimates for the mean.
Answers:
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a.No, since the sample means will be normally
distributed by the central limit theorem.
b. 5.4545
c. 280
d. 273.02 to 286.98 271.05 to 288.95
39. The makers of a soft drink want to identify
the average age of its consumers. A sample of
16 consumers is taken. The average age in the
sample was 22.5 years with a standard deviation
of 5 years.
a. Construct a 95% confidence interval for the
true average age of the consumers.
b. Construct an 80% confidence interval for the
true average age of the consumers.
c. Discuss why the 95% and 80% confidence
intervals are different.
Answers:
a. 19.836 to 25.164
b. 20.824 to 24.176
c. As the level of confidence increases, the
confidence interval gets wider.
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