Deck 9: Estimation and Confidence Intervals

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

If the size of a sample equals the size of the population,we would not expect any error in estimating the population parameter.

Question 5

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

Question 6

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 7

The t distribution is a continuous distribution.

Question 8

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

Question 9

There is not one t distribution,but rather a "family" of t distributions.

Question 10

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 11

A distribution of sample means is normally distributed with a mean equal to the population mean and a standard deviation equal to the standard error of the mean.

Question 12

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

Question 13

The Central Limit Theorem proves that the sampling distribution of sample means tends to approximate a normal distribution when the sample size becomes larger.

Question 14

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

Question 15

One factor in determining the size of a sample is the maximum allowable error that you must decide on.It is the maximum error you will tolerate at a specified level of confidence.

Question 16

The higher the degree of confidence,the larger the sample required to give a certain precision.

Question 17

The t distribution is positively skewed.

Question 18

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

Question 19

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 20

We can expect a difference between a sample statistic and the corresponding population parameter.This difference is called the sampling error.

Question 21

The test statistic for a problem involving any sample size and an unknown population standard deviation is the Student's t distribution.

Question 22

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 23

What kind of distribution is the t distribution?

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

Question 24

The Student t distribution has a greater spread than the z distribution.As a result,the critical values of t for a given level of significance are larger than the corresponding z critical values.

Question 25

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 26

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

Question 27

William S.Gosset,a brewmaster,developed the t test for the Guiness Brewery in Ireland and published it in 1908 using the pen name "Student."

Question 28

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

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

Question 29

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 30

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 31

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 32

All t distributions have a mean of zero and a standard deviation of 1.

Question 33

The test statistic t has n - 1 degrees of freedom.

Question 34

The t distribution is more spread out and flatter at the center than the standard normal distribution.However,as the sample size increases,the t distribution curve approaches the standard normal distribution.

Question 35

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 36

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 37

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 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

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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 47

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 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.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 50

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 51

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 52

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 53

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 54

The distribution of Student's t is

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

Question 55

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 56

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 57

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 58

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 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 59

A sample mean is the best point estimate of the

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

Question 60

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 61

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 62

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 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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 71

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

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

Question 72

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 73

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 74

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 75

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 76

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 77

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 78

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 79

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 80

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]