Deck 9: Estimation and Confidence Intervals

Question 1

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

Answer 1

87

Question 2

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 2

133

Question 3

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

Answer 3

6.14 and 6.86

Question 4

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

Question 5

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

Question 6

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

A)σ
B)x/n
C)
D)s

Question 7

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 8

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

Question 9

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

Question 10

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 11

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 12

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 13

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 14

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

Question 15

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 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

What kind of distribution is the t distribution?

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

Question 29

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 30

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 31

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 32

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 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

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 35

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 36

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 37

The distribution of Student's t is ________.

A)Symmetrical
B)Negatively skewed
C)Positively skewed
D)A discrete probability distribution

Question 38

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 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

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 41

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

Question 44

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 45

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 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 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 47

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 48

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 49

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 50

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 51

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 52

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 53

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)70% is not in the interval, so another sample is needed.
B)70% 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 population, we cannot make a conclusion.

Question 54

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 55

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 56

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 57

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 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 58

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 59

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 60

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 61

A 95% confidence interval implies that about 95 out of 100 similarly constructed intervals will include the _____________ being estimated.

Question 62

The interval within which a population parameter is expected to lie is called a __________.

Question 63

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)[0.767, 0.814]
B)[0.655, 0.705]
C)[0.644, 0.716]
D)[0.680, 0.681]

Question 64

A(n) _________ estimate states the range within which a population parameter probably lies.

Question 65

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 66

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 67

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

Question 68

Making generalized statements about a population based on sample information is called _________________.

Question 69

Assuming a normal population with a known population standard deviation, the z statistic for a 90% confidence interval would be ____.

Question 70

For a distribution of sample means with a known population standard deviation, about _____ percent of the sample means are within three standard errors of population mean.

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

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

Question 73

For a distribution of sample means with a known population standard deviation, about _____ percent of the sample means are within one standard error of population mean.

Question 74

Other things being equal, a smaller sample size would result in a wider confidence interval because the standard error of the mean is ______________.

Question 75

The probability that an interval estimate includes the population parameter is called the _____________.

Question 76

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 77

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)[0.6569, 0.7031]
C)[0.6659, 0.6941]
D)[0.6795, 0.6805]

Question 78

For a sampling distribution of means with a known population standard deviation, ______% of the means would be between ±1.96 standard errors.

Question 79

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

Question 80

Assuming a normal population with a known population standard deviation, the z statistic for a 99% confidence interval would be ______.