Deck 9: Estimation and Confidence Intervals

Question 1

A point estimate is a range of values used to estimate a population parameter.

Answer 1

False

Question 2

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?

A) 14.7 and 16.9
B) 13.2 and 17.6
C) 10.0 and 20.0
D) 16.1 and 18.1

Answer 2

A

Question 3

The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.90 degree of confidence. For a small pilot study, the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days, how many salespeople should be sampled?

A) 133
B) 452
C) 511
D) 2,100

Answer 3

A

Question 4

A confidence interval for a population proportion uses the uniform distribution to approximate the binomial distribution.

Question 5

A sample of 2,000 union members was selected, and a survey recorded their opinions regarding a proposed management union contract. A total of 1,600 members were in favor of it. A 95% confidence interval estimated that the population proportion was between 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

Question 6

One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99, but it may be any degree of confidence you specify.

Question 7

The population variation has little or no effect in determining the size of a sample selected from the population.

Question 8

To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

Question 9

A z statistic is used for a problem involving any sample size and an unknown population standard deviation.

Question 10

An interval estimate is a range of values used to estimate a population parameter.

Question 11

The finite population correction factor is used to adjust the z-statistic.

Question 12

A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

A) 6.99 and 7.99
B) 4.15 and 7.15
C) 6.14 and 6.86
D) 6.49 and 7.49

Question 13

An interval estimate is a single value used to estimate a population parameter.

Question 14

A point estimate is a single value used to estimate a population parameter.

Question 15

To determine the value of the standard error of the mean, the standard deviation is divided by the sample size.

Question 16

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?

A) 0.647 and 0.753
B) 0.612 and 0.712
C) 0.397 and 0.797
D) 0.826 and 0.926

Question 17

When using the t distribution to calculate a confidence interval, we assume that the population of interest is normal or nearly normal.

Question 18

A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 0.95 degree of confidence is to be used. Several years ago, a study revealed that 21% of junior executives left their company within three years. To update this study, how many junior executives should be surveyed?

A) 594
B) 612
C) 709
D) 897

Question 19

The finite population correction factor is applied when the population size is known.

Question 20

The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

Question 21

When using Student's t to compute an interval estimate, ___________.

A) we assume that the samples are collected from populations that are uniformly distributed
B) we estimate the population mean based on the sample mean
C) we use the z distribution
D) we assume that the samples are collected from normally distributed populations

Question 22

Which statement(s) is/are correct about the t distribution?

A) The mean is zero.
B) Its shape is symmetric.
C) Its dispersion is based on degrees of freedom.
D) All apply.

Question 23

A sample mean is the best point estimate of _______.

A) the population standard deviation
B) the population median
C) the population mean
D) the sample standard deviation

Question 24

Of the following characteristics, the t distribution and z distribution are the same in all BUT one. Which one is it?

A) Continuous
B) Symmetrical
C) Bell-shaped
D) Mean = 0, and standard deviation = 1

Question 25

When a confidence interval for a population mean is constructed from sample data, __________.

A) we can conclude that the population mean is in the interval
B) we can conclude that the population mean is not in the interval
C) we can conclude, for an infinite number of samples and corresponding confidence intervals, that the population mean is in a stated percentage of the intervals
D) we cannot make any inferences

Question 26

A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what number of degrees of freedom should be used to determine the appropriate t-value?

A) 20
B) 19
C) 21
D) 25

Question 27

The distribution of Student's t has _________.

A) a mean of zero and a standard deviation of one
B) a mean of one and a standard deviation of one
C) a mean of zero and a standard deviation that depends on the sample size
D) a mean that depends on the sample size and a standard deviation of one

Question 28

Knowing the population standard deviation, a 95% confidence interval infers that the population mean ___________.

A) is between 0 and 100%
B) is within ±1.96 standard deviations of the sample mean
C) is within ±1.96 standard errors of the sample mean
D) is too large

Question 29

How is the t distribution similar to the standard z distribution?

A) Both are discrete distributions.
B) Both are skewed distributions.
C) Both are families of distributions.
D) Both are continuous distributions.

Question 30

What kind of distribution is the t distribution?

A) Continuous
B) Discrete
C) Subjective
D) A z distribution

Question 31

A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?

A) 5.04 and 5.96
B) 5.06 and 5.94
C) 2.67 and 8.33
D) 4.40 and 6.60

Question 32

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?

A) 50,000
B) 3,500
C) 500
D) 35

Question 33

Which of the following is NOT necessary to determine how large a sample to select from a population?

A) The level of confidence in estimating the population parameter
B) The size of the population
C) The maximum allowable error in estimating the population parameter
D) An estimate of the population variation

Question 34

The distribution of Student's t is ________.

A) symmetrical
B) negatively skewed
C) positively skewed
D) a discrete probability distribution

Question 35

Which of the following is a point estimate for the population mean (µ)?

A) σ
B) x/n
C)
D) s

Question 36

A sample standard deviation is the best point estimate of the ___________.

A) population range
B) population skewness
C) population mode
D) population standard deviation

Question 37

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10^th of a percent)?

A) 78.2% to 81.8%
B) 69.2% to 86.4%
C) 76.5% to 83.5%
D) 77.7% to 82.3%

Question 38

What is the interpretation of a 96% confidence level?

A) There's a 96% chance that the given interval includes the true value of the population parameter.
B) Approximately 96 out of 100 such intervals would include the true value of the population parameter.
C) There's a 4% chance that the given interval does not include the true value of the population parameter.
D) The interval contains 96% of all sample means.

Question 39

A confidence interval for a population mean __________.

A) estimates the population range
B) estimates a likely interval for a population mean
C) estimates likelihood or probability
D) estimates the population standard deviation

Question 40

A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an interval of $75 is desired, how many customers should be sampled?

A) 44
B) 212
C) 629
D) 87

Question 41

A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

A) $323.40 to $426.60
B) $328.40 to $421.60
C) $350.80 to $395.80
D) $369.31 to $380.69

Question 42

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000, with a standard deviation of $2,500. What is the best point estimate of the population mean?

A) $25,000
B) $2,500
C) $400
D) $62.5

Question 43

A local company wants to evaluate their quality of service by surveying their customers. Their budget limits the number of surveys to 100. What is their maximum error of the estimated mean quality for a 95% level of confidence and an estimated standard deviation of 5?

A) 0.9604
B) 0.98
C) 1.96
D) 5%

Question 44

A group of statistics students decided to conduct a survey at their university to estimate the average (mean) amount of time students spent studying per week. They sampled 554 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the 95% level of confidence?

A) [21.80, 22.80]
B) [16.3, 28.3]
C) [21.64, 22.96]
D) [20.22, 22.0]

Question 45

A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave, what similarities would they have?

A) Both have the same confidence level
B) Both use the same t statistic
C) Both use the same z statistic
D) Both use the same point estimate of the population mean

Question 46

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation was $2,500. What is the 95% confidence interval for the mean salary of all graduates from the English Department?

A) [$22,500, $27,500]
B) [$24,755, $25,245]
C) [$24,988, $25,012]
D) [$24,600, $25,600]

Question 47

A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase?

A) [0.767, 0.815]
B) [0.759, 0.822]
C) [0.771, 0.811]
D) [0.714, 0.866]

Question 48

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 99% confidence interval to estimate the true cost of the microwave?

A) $367.42 to $382.58
B) $315.00 to $415.00
C) $323.40 to $426.60
D) $335.82 to $414.28

Question 49

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the 99% level of confidence?

A) [21.80, 22.80]
B) [16.3, 28.3]
C) [21.30, 23.30]
D) [20.22, 22.0]

Question 50

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of six hours, what is the required sample size if the error should be less than a half hour with a 95% level of confidence?

A) 554
B) 130
C) 35
D) 393

Question 51

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation is $2,500. A 95% confidence interval is constructed. What does the confidence interval mean?

A) The population mean is in the interval.
B) The population mean is not in the interval.
C) The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95.
D) There is a 5% chance that the computed interval does not contain the population mean.

Question 52

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the best point estimate for the population mean?

A) 2.1 years
B) 1.5 years
C) 19.1 years
D) 9 years

Question 53

A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour?

A) 196
B) 98
C) 10
D) 16

Question 54

University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75, 0.85], what conclusion can be drawn?

A) Seventy percent is not in the interval, so another sample is needed.
B) Seventy percent is not in the interval, so assume it will not be supported.
C) The interval estimate is above 70%, so infer that it will be supported.
D) Since this was not based on the population, no conclusion can be drawn.

Question 55

A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 99% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase?

A) [0.751, 0.829]
B) [0.759, 0.823]
C) [0.767, 0.814]
D) [0.771, 0.811]

Question 56

When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called __________.

A) descriptive statistics
B) the normal distribution
C) statistical inference
D) graphics

Question 57

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence?

A) 196
B) 239
C) 15
D) 16

Question 58

A local retail company wants to estimate the mean amount spent by customers. Their store's budget limits the number of surveys to 225. What is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00?

A) $10.00
B) $1.00
C) 1%
D) $1.72

Question 59

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?

A) [0.97, 3.27]
B) [15.64, 22.56]
C) [17.97, 20.23]
D) [17.95, 20.25]

Question 60

If 95% and 98% confidence intervals were developed to estimate the true cost of an MP3 player with a known population standard deviation, what differences would they have?

A) The standard errors would be different.
B) The point estimates of the population mean would be different.
C) The sample sizes would be different.
D) The z statistics would be different.

Question 61

A sample of 500 students is selected from a known population of 15000 students to construct a 99% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?

A) 0.9499
B) 0.9832
C) 2.5760
D) Cannot be determined

Question 62

A sample of 25 is selected from a known population of 100 elements. What is the finite population correction factor?

A) 8.66
B) 75
C) 0.87
D) Cannot be determined

Question 63

A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean (x-bar) is 300. What is the margin of error at the 95% confidence level?

A) 8
B) 293
C) 7
D) 308

Question 64

A sample of 100 is selected from a known population of 350 elements. The population standard deviation is 15. Using the finite correction factor, what is the standard error of the sample means?

A) 12.6773
B) 0.8452
C) 1.2695
D) Cannot be determined

Question 65

A student wanted to construct a 99% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean?

A) [17.42, 20.78]
B) [17.48, 20.72]
C) [14.23, 23.98]
D) [0.44, 3.80]

Question 66

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a gallon of milk?

A) $2.81 to $3.15
B) $2.94 to $3.02
C) $2.77 to $3.19
D) $2.95 to $3.01

Question 67

A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence, what is the confidence interval for the proportion of students attending a football game?

A) [0.7510, 0.8290]
B) [0.6591, 0.7045]
C) [0.6659, 0.6941]
D) [0.6795, 0.6805]

Question 68

A sample of 50 is selected from a known population of 250 elements. The population standard deviation is 15. Using the finite correction factor, what is the standard error of the sample means?

A) 2.89
B) 1.90
C) 2.12
D) Cannot be determined

Question 69

A sample of 100 students is selected from a known population of 1000 students to construct a 95% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?

A) 0.949
B) 0.901
C) 1.96
D) Cannot be determined

Question 70

Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________.

A) [0.541, 0.639]
B) [0.400, 0.600]
C) [0.500, 0.700]
D) [0.565, 0.635]

Question 71

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk, what similarities would they have?

A) Both have the same confidence level
B) Both use the same t statistic
C) Both use the same z statistic
D) Both use the same point estimate of the population mean

Question 72

A sample mean is a _______________ estimate of the population mean.

Question 73

As the sample size for a t distribution increases, the differences between the t distribution and the standard normal distribution:

A) are unchanged and remain the same.
B) become smaller, as the t distribution approaches the standard normal distribution.
C) become greater.
D) are evident because the tails of the t distribution become thicker.

Question 74

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?

A) $2.73 to $3.23
B) $2.85 to $3.11
C) $2.94 to $3.02
D) $2.95 to $3.01

Question 75

A survey of households in a small town showed that in 500 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 95% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?

A) [0.417, 0.427]
B) [0.389, 0.445]
C) [0.400, 0.417]
D) [0.417, 0.445]

Question 76

A survey of households in a small town showed that in 850 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 99% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?

A) [0.674, 0.742]
B) [0.655, 0.705]
C) [0.665, 0.694]
D) [0.679, 0.680]

Question 77

When estimating a population mean with a confidence interval, a smaller margin of error requires a _________ sample size.

Question 78

The z-score or z-value corresponding to a 95.34% confidence interval is ________.

A) 1.96
B) 1.65
C) 1.99
D) 1.68

Question 79

A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 99% level of confidence, what is the confidence interval for the proportion of students attending a football game?

A) [0.7671, 0.8143]
B) [0.6550, 0.7050]
C) [0.6464, 0.7172]
D) [0.6805, 0.6815]

Question 80

To calculate the sample size required to estimate a population mean, we must know or estimate the ______________ of the population distribution.