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

A random sample of 85 group leaders and 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 2

C

Question 3

The test statistic for a problem involving any sample size and an unknown population standard deviation is the z distribution.

Answer 3

False

Question 4

There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned 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 5

The population variation as measured by the standard deviation has little or no effect in determining the size of a sample selected from the population.

Question 6

A confidence interval for a population proportion is based on using the uniform distribution to approximate the binomial distribution.

Question 7

The 95 percent confidence interval states that 95 percent 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

The mean number of travel days per year for salespeople employed by 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) 134
B) 452
C) 511
D) 2100

Question 9

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 mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95 percent 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 10

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

Question 11

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 12

The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21. To update this study, the files of how many junior executives should be studied?

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

Question 13

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 14

A sample of 2000 union members was selected and their opinions regarding a proposed management union contract were recorded. 1,600 members were in favor of it. A 95% confidence interval for the population proportion was computed to be 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

The t distribution is based on the assumption that the population of interest is normal or nearly normal.

Question 21

A random sample of 20 items is selected from a population. To determine the appropriate critical t-value what number of degrees of freedom should be used?

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

Question 22

What kind of distribution is the t distribution?

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

Question 23

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

A) 50,000
B) 3,500
C) (50,000/100)
D) (3,500/100)

Question 24

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 25

The distribution of Student's t is

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

Question 26

For a given confidence interval, what is the interpretation of a 96% confidence level?

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) 4% chance that the given interval does not include the true value of the population parameter
D) Both a and c are true

Question 27

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

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

Question 28

A 95% confidence interval infers that the population mean

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

Question 29

Which of the following would be used as a point estimate for the population mean ( µ )?

A) $\sigma$
B)
C)
D) s

Question 30

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 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

The t distribution is similar to the z distribution in all BUT one of the following characteristics. Which one is it?

A) Continuous
B) Symmetrical
C) Bell-shaped
D) t distribution's mean = 0 and standard deviation = 1

Question 33

A confidence interval for a population mean

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

Question 34

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 percent 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 35

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

A) Level of confidence in estimating the population parameter
B) Size of the population
C) Maximum allowable error in estimating the population parameter
D) Estimate of the population variation

Question 36

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

A) Both are continuous distribution
B) Both are bell-shaped
C) Both are families of distributions
D) A and B

Question 37

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 38

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

A) Mean = 0
B) Symmetric
C) Based on degrees of freedom
D) All of these are correct

Question 39

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 40

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 tenth 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 41

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 6 hours, what is the required sample size if the error should be less than ½ hour with a 95% level of confidence?

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

Question 42

If university officials say that at least 70% of the voting student population supporting the fee increase, if the 95% confidence interval is [0.75, 0.85], what conclusion can be drawn based on a 95% level of confidence?

A) 70% is not in the interval, need to take another sample
B) 70% is not in the interval, so assume it will not be supported
C) 70% is below the interval, so assume it will be supported
D) Since this was not based on population, cannot make conclusion

Question 43

A survey of an urban university (population of 25,450) showed that 870 of 1100 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) [0.758, 0.822]
C) [0.767, 0.814]
D) [0.771, 0.811]

Question 44

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 45

Recently, 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. 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 46

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 6 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 47

A local retail company wants to estimate the mean amount spent. Their 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 48

A survey of an urban university (population of 25,450) showed that 870 of 1100 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, 0.814]
B) [0.759, 0.822]
C) [0.771, 0.811]
D) [0.714, 0.866]

Question 49

Recently, 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 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 3 hours, what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?

A) 196
B) 240
C) 15
D) 16

Question 51

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

A) Point estimates
B) Z-variates
C) Standard errors
D) Both "a" and "c"

Question 52

Recently, 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 53

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) 0.9920
C) 1.96
D) 5%

Question 54

A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The population 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 55

If 95% and 98% confidence intervals were developed to estimate the true cost of a MP3 player microwave, what differences would they have?

A) Standard errors
B) Interval widths
C) Z-statistic
D) Both b and c

Question 56

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error 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 57

Assuming a population standard deviation of 3 hours, what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?

A) 196
B) 240
C) 15
D) 16

Question 58

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 6 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 59

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a 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 60

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error 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 61

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a 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 62

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

Question 63

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 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 64

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. If 90% and 95% confidence intervals are developed to estimate the true cost of a gallon of milk, what similarities would they have?

A) Point estimates
B) t-statistics
C) Standard errors
D) Both a and c

Question 65

A finite population correction factor is used when we know the _________________.

Question 66

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 67

A sample mean is a _______________ of the population mean.

Question 68

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 69

A survey of an urban university (population of 25,450) showed that 750 of 1100 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) [0.6620, 0.6980]
C) [0.6659, 0.6941]
D) [0.6795, 0.6805]

Question 70

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 71

A survey of an urban university (population of 25,450) showed that 750 of 1100 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) [0.6550, 0.7050]
C) [0.6659, 0.6941]
D) [0.6795, 0.6805]

Question 72

A survey of households in a small town showed of 1200 sampled households, that in 850 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) [0.6745, 0.7421]
B) [0.6550, 0.7050]
C) [0.6659, 0.6941]
D) [0.6795, 0.6805]

Question 73

A survey of households in a small town showed of 1200 sampled households, that in 500 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) [0.4167, 0.4267]
B) [0.3888, 0.4446]
C) [0.4000, 0.4167]
D) [0.4167, 0.4446]

Question 74

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 75

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a 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 76

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 77

A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people. Forty sales people were randomly selected. Their mean monthly sales was $10,000 with a population standard deviation of $1000. Construct a 95% confidence interval for the population mean.

A) [9,690.1, 10,309.9]
B) [9,715.5, 10,284.5]
C) [8,040, 11,960]
D) [8,000, 12,000]

Question 78

To calculate the sample size required to estimate a population mean, smaller margins of error require ______________ sample sizes.

Question 79

A finite population correction factor is used to adjust the _________________.

Question 80

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