Deck 8: Interval Estimation

Question 1

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed

A).05
B)5
C)10
D)30

Answer 1

5

Question 2

An estimate of a population parameter that provides an interval 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 2

interval estimate

Question 3

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 3

0.95

Question 4

The mean of the t distribution is

A)0
B).5
C)1
D)problem specific

Question 5

An interval estimate is used to estimate

A)the shape of the population's distribution
B)the sampling distribution
C)a sample statistic
D)a population parameter

Question 6

If the margin of error in an interval estimate of $\mu$ is 4.6, the interval estimate equals

A)
B)
C)
D)

Question 7

We can reduce the margin of error in an interval estimate of p by doing any of the following except

A)increasing the sample size
B)increasing the planning value p* to .5
C)increasing the level of significance
D)reducing the confidence coefficient

Question 8

The z value for a 97.8% confidence interval estimation is

A)2.02
B)1.96
C)2.00
D)2.29

Question 9

The ability of an interval estimate to contain the value of the population parameter is described by the

A)confidence level
B)degrees of freedom
C)precise value of the population mean $\mu$
D)None of the other answers are correct.

Question 10

The expression used to compute an interval estimate of $\mu$ may depend on any of the following factors except

A)the sample size
B)whether the population standard deviation is known
C)whether the population has an approximately normal distribution
D)whether there is sampling error

Question 11

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to

A).01
B).50
C).51
D).99

Question 12

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be

A)0.1
B)0.95
C)0.9
D)0.05

Question 13

In determining an interval estimate of a population mean when $\sigma$ is unknown, we use a t distribution with

A) degrees of freedom
B) degrees of freedom
C)n- 1 degrees of freedom
D)n degrees of freedom

Question 14

The confidence associated with an interval estimate is called the

A)level of significance
B)degree of association
C)confidence level
D)precision

Question 15

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

A)level of significance
B)confidence level
C)confidence coefficient
D)error factor

Question 16

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

A)finite correction factor
B)sample size
C)degrees of freedom
D)standard deviation

Question 17

As the sample size increases, the margin of error

A)increases
B)decreases
C)stays the same
D)None of the other answers are correct.

Question 18

As the degrees of freedom increase, the t distribution approaches the

A)uniform distribution
B)normal distribution
C)exponential distribution
D)p distribution

Question 19

To compute the minimum sample size for an interval estimate of $\mu$ , we must first determine all of the following except

A)desired margin of error
B)confidence level
C)population standard deviation
D)degrees of freedom

Question 20

For the interval estimation of $\mu$ when $\sigma$ is assumed known, the proper distribution to use is the

A)standard normal distribution
B)t distribution with n degrees of freedom
C)t distribution with n - 1 degrees of freedom
D)t distribution with n - 2 degrees of freedom

Question 21

A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?

A)95% of the sample of employees has a systolic blood pressure between 123 and 139.
B)If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
C)95% of the population of employees has a systolic blood pressure between 123 and 139.
D)If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

Question 22

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for $\mu$

A)becomes narrower
B)becomes wider
C)does not change
D)becomes 0.1

Question 23

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A)becomes larger
B)becomes smaller
C)stays the same
D)None of the other answers are correct.

Question 24

A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for $\mu$ is

A)6.000 to 14.000
B)9.846 to 10.154
C)8.384 to 11.616
D)8.462 to 11.538

Question 25

A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is

A)70.02 to 81.98
B)69.82 to 82.18
C)70.06 to 81.94
D)69.48 to 82.52

Question 26

From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for $\mu$ . Which of the following statements is true?

A)The standard normal distribution can be used.
B)The t distribution with 50 degrees of freedom must be used.
C)The t distribution with 49 degrees of freedom must be used.
D)The sample size must be increased in order to develop an interval estimate.

Question 27

The t distribution should be used whenever

A)the sample size is less than 30
B)the sample standard deviation is used to estimate the population standard deviation
C)the population is not normally distributed
D)None of the other answers are correct.

Question 28

Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean?

A)standard distribution
B)z distribution
C)binomial distribution
D)t distribution

Question 29

Whenever using the t distribution in interval estimation, we must assume that the

A)sample size is less than 30
B)degrees of freedom equals n - 1
C)population is approximately normal
D)finite population correction factor is necessary

Question 30

An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random sample of 200 current owners is taken. The population standard deviation is known. Which Excel function would not be appropriate to use to construct a confidence interval estimate?

A)NORM.S.INV
B)COUNTIF
C)AVERAGE
D)STDEV.S

Question 31

A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the college are normally distributed with a standard deviation of 1.8 years. The 98% confidence interval for the average age of all students at this college is

A)24.301 to 25.699
B)24.385 to 25.615
C)23.200 to 26.800
D)23.236 to 26.764

Question 32

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)19.2 to 20.8
C)19.216 to 20.784
D)21.2 to 22.8

Question 33

A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50 times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2 minutes. Which Excel function would be used to construct a confidence interval estimate?

A)CONFIDENCE.NORM
B)NORM.INV
C)T.INV
D)INT

Question 34

From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of $\mu$ , the proper distribution to use is the

A)standard normal distribution
B)z distribution
C)t distribution with 26 degrees of freedom
D)t distribution with 24 degrees of freedom

Question 35

The t value with a 95% confidence and 24 degrees of freedom is

A)1.711
B)2.064
C)2.492
D)2.069

Question 36

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of

A)7.84 or less
B)31.36 or less
C)344.96 or less
D)1,936 or less

Question 37

In developing an interval estimate of the population mean, if the population standard deviation is unknown

A)it is impossible to develop an interval estimate
B)a sample proportion can be used
C)the sample standard deviation and t distribution can be used
D)None of the other answers are correct.

Question 38

In general, higher confidence levels provide

A)wider confidence intervals
B)narrower confidence intervals
C)a smaller standard error
D)unbiased estimates

Question 39

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the

A)width of the confidence interval to increase
B)width of the confidence interval to decrease
C)width of the confidence interval to remain the same
D)sample size to increase

Question 40

When the level of confidence increases, the confidence interval

A)stays the same
B)becomes wider
C)becomes narrower
D)cannot tell from the information given

Question 41

Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute.
Refer to Exhibit 8-2. The standard error of the mean equals

A)0.001
B)0.010
C)0.100
D)1.000

Question 42

Exhibit 8-1
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.
Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately

A)7.04 to 110.96 hours
B)7.36 to 10.64 hours
C)7.80 to 10.20 hours
D)8.74 to 9.26 hours

Question 43

A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is taken. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate?

A)NORM.S.INV
B)NORM.INV
C)T.INV
D)INT

Question 44

For which of the following values of p is the value of p(1 - p) maximized?

A)p = 0.99
B)p = 0.90
C)p = 1.0
D)p = 0.50

Question 45

Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute.
Refer to Exhibit 8-2. If the confidence coefficient is reduced to 0.80, the standard error of the mean

A)will increase
B)will decrease
C)remains unchanged
D)becomes negative

Question 46

Using an $\alpha$ = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

A)becomes narrower
B)becomes wider
C)does not change
D)Not enough information is provided to answer this question.

Question 47

Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute.
Refer to Exhibit 8-2. With a .95 probability, the sample mean will provide a margin of error of

A)0.95
B)0.10
C).196
D)1.96

Question 48

In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?

A)the maximum margin of error that can be tolerated
B)the confidence level required
C)a preliminary estimate of the true population proportion p
D)the mean of the population

Question 49

The degrees of freedom associated with a t distribution are a function of the

A)area in the upper tail
B)sample standard deviation
C)confidence coefficient
D)sample size

Question 50

Exhibit 8-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute.
Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time of all customers is

A)3 to 5
B)1.36 to 4.64
C)2.804 to 3.196
D)1.04 to 4.96

Question 51

Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.
Refer to Exhibit 8-3. The value to use for the standard error of the mean is

A)13.5
B)9
C)2.26
D)1.5

Question 52

A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random sample of 50 items is taken. Which Excel function would not be appropriate to construct a confidence interval estimate?

A)NORM.S.INV
B)COUNTIF
C)STDEV
D)All are appropriate.

Question 53

The margin of error in an interval estimate of the population mean is a function of all of the following except

A)level of significance
B)sample mean
C)sample size
D)variability of the population

Question 54

Exhibit 8-1
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.
Refer to Exhibit 8-1. With a 0.95 probability, the margin of error is approximately

A)0.26
B)1.96
C)0.21
D)1.64

Question 55

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when

A)np $\ge$ 5
B)n(1 - p) $\ge$ 5
C)p has a normal distribution
D)Both np $\ge$ 5 and n(1 - p) $\ge$ 5

Question 56

Exhibit 8-1
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.
Refer to Exhibit 8-1. The standard error of the mean is

A)7.5
B)0.014
C)0.160
D)0.133

Question 57

To estimate a population mean, 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

Question 58

Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.

-Refer to Exhibit 8-3. If we are interested in determining an interval estimate for $\mu$ at 86.9% confidence, the z value to use is

A)1.96
B)1.31
C)1.51
D)2.00

Question 59

The general form of an interval estimate of a population mean or population proportion is the _____ plus and minus the _____.

A)population mean, standard error
B)level of significance, degrees of freedom
C)point estimate, margin of error
D)planning value, confidence coefficient

Question 60

It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is

A)25
B)74
C)189
D)75

Question 61

A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes.

A)Compute the standard error of the mean.
B)What can be said about the sampling distribution for the average amount of time customers spent in the restaurant? Be sure to explain your answer.
C)With a .95 probability, what statement can be made about the size of the margin of error?
D)Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant.
E)With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?

Question 62

A random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. The balances of all checking accounts at the bank are normally distributed. Develop a 95% confidence interval estimate for the mean of the population.

Question 63

A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term. The population standard deviation is known to be 1.8 days. Provide a 90% confidence interval for the average number of days absent per term for all the children.

Question 64

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000.
a.Provide a 95% confidence interval estimate for the average daily sale.
b.Provide a 97% confidence interval estimate for the average daily sale.

Question 65

A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes with a standard deviation of 10 minutes before they could see the doctor. Provide a 98% confidence interval estimate for the average waiting time of all the patients who visit this doctor. Assume the population of waiting times is normally distributed.

Question 66

A sample of 16 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages is normally distributed.

Question 67

A random sample of 81 students at a local university showed that they work an average of 100 hours per month. The population standard deviation is known to be 27 hours. Compute a 95% confidence interval for the mean hours per month all students at the university work.

Question 68

A simple random sample of 144 items resulted in a sample mean of 1080. The population standard deviation is known to be 240. Develop a 95% confidence interval for the population mean.

Question 69

Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.

-Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for $\mu$ would

A)not change
B)become narrower
C)become wider
D)become zero

Question 70

Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.

-Refer to Exhibit 8-3. The 86.9% confidence interval for $\mu$ is

A)46.500 to 73.500
B)57.735 to 62.265
C)59.131 to 60.869
D)50 to 70

Question 71

Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 196 transactions yielded a mean of 5 seconds. The population standard deviation is 1.4 seconds. Determine a 97% confidence interval for the average CPU time.

Question 72

In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours. The standard deviation is 3.2 hours per week for all freshman college students.
a.Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.
b.Suppose the sample mean came from a sample of 25 students. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Assume that the hours are normally distributed.

Question 73

The average monthly electric bill of a random sample of 256 residents of a city is $90. The population standard deviation is assumed to be $24.
a.Construct a 90% confidence interval for the mean monthly electric bills of all residents.
b.Construct a 95% confidence interval for the mean monthly electric bills of all residents.

Question 74

A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounces.

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.

Question 75

A random sample of 36 magazine subscribers is taken to estimate the mean age of all subscribers. The data follow. Use Excel to construct a 90% confidence interval estimate of the mean age of all of this magazine's subscribers.

Question 76

The Highway Safety Department wants to study the driving habits of individuals. A sample of 41 cars traveling on the highway revealed an average speed of 60 miles per hour and a standard deviation of 7 miles per hour. The population of car speeds is approximately normally distributed. Determine a 90% confidence interval estimate for the speed of all cars.

Question 77

In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined.
a.Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean.
b.With a 0.95 probability, determine the margin of error.
c.If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?

Question 78

A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00.
a.Determine the standard error of the mean.
b.With a 0.95 probability, determine the margin of error.
c.What is the 95% confidence interval of the population mean?

Question 79

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds.
a.Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b.Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

Question 80

A simple random sample of 25 items from a normally distributed population resulted in a sample mean of 28 and a standard deviation of 7.5. Construct a 95% confidence interval for the population mean.