Deck 7: Confidence Intervals and Sample Size

Question 1

An economics professor randomly selected 100 millionaires in the United States. The average age of these millionaires was 54.8 years. If the standard deviation of the entire population of millionaires is 7.9 years, find the 95% confidence interval for the mean age of all United States millionaires.

A)
B)
C)
D)

Answer 1

C

Question 2

A sample of 35 different payroll departments found that employees worked an average of 240.6 days a year. If the population standard deviation is 18.8 days, find the 90% confidence interval for the average number of days worked by all employees who are paid through payroll departments.

A)
B)
C)
D)

Answer 2

C

Question 3

The formula for the confidence interval of the mean for a specific is ____________________.

Answer 3

Question 4

If a population has a standard deviation of 16, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 3 of the true mean?

A) 216
B) 11
C) 110
D) 22

Question 5

A study of peach trees found that the average number of peaches per tree was 525. The standard deviation of the population is 105 peaches per tree. A scientist wishes to find the 80% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 12 peaches per tree?

A) 77
B) 55
C) 83
D) 126

Question 6

A study of 65 bolts of carpet showed that their average length was 76.2 yards. The standard deviation of the population is 2.6 yards. Which of the following is the 80% confidence interval for the mean length per bolt of carpet?

A)
B)
C)
D)

Question 7

The term
describes the ___________________.

A) unbiased estimator
B) confidence interval
C) maximum error of estimate
D) interval estimate

Question 8

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

Question 9

According to a study of 90 truckers, a trucker drives, on average, 540 miles per day. If the standard deviation of the miles driven per day for the population of truckers is 40, find the 99% confidence interval of the mean number of miles driven per day by all truckers.

Question 10

The average score for 49 teenage boys playing a certain computer game was 80,000 points per player. If the standard deviation of the population is 20,000 points, find the 95% confidence interval of the mean score for all teenage boys.

Question 11

A random sample of magnesium concentrations (in parts per million, or ppm) in ground water from various locations follows. Estimate the mean concentration of magnesium in ppm with 90% confidence. Assume .

A)
B)
C)
D)

Question 12

A student looked up the number of years served by 35 of the more than 100 Supreme Court justices. The average number of years served by those 35 justices was 13.8. If the standard deviation of the entire population is 7.3 years, find the 95% confidence interval for the average number of years served by all Supreme Court justices.

A)
B)
C)
D)

Question 13

An interval estimate may or may not contain the true value of the parameter being estimated.

Question 14

A study of 50 white mice showed that their average weight was 4.2 ounces. The standard deviation of the population is 0.7 ounces. Which of the following is the 90% confidence interval for the mean weight per white mouse?

A)
B)
C)
D)

Question 15

A study of 45 professors showed that the average time they spent creating test questions was 15.5 minutes per question. The standard deviation of the population is 5.8. Which of the following is the 98% confidence interval for the average number of minutes it takes to create a test question?

A)
B)
C)
D)

Question 16

The average number of mosquitos caught in 81 mosquito traps in a particular environment was 900 per trap. The standard deviation of mosquitos caught in the entire population of traps is 150 mosquitos. What is the 99% confidence interval for the true mean number of mosquitos caught in all mosquito traps?

Question 17

A study of 75 apple trees showed that the average number of apples per tree was 925. The standard deviation of the population is 100. Which of the following is the 95% confidence interval for the mean number of apples per tree for all trees?

A)
B)
C)
D)

Question 18

The ______________________ is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter.

Question 19

What value of is used in confidence interval shown below?

Question 20

When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.

Question 21

In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is

A) a standard normal distribution.
B) a t distribution with 7 degrees of freedom.
C) a t distribution with 8 degrees of freedom.
D) a t distribution with 9 degrees of freedom.

Question 22

A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet?

A)
B)
C)
D)

Question 23

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence.

A)
B)
C)
D)

Question 24

Find when n = 23 for the 99% confidence interval for the mean.

A) 2.82
B) 2.51
C) 1.94
D) 3.46

Question 25

One of the characteristics of the t-distribution is that the curve never touches the ____-axis.

Question 26

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes.

Question 27

The _________________ are the number of values that are free to vary after a sample statistic has been computed.

Question 28

In a study of 100 new cars, 30 are white. Find and , where is the proportion of new cars that are white.

A)
B)
C)
D)

Question 29

A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.

A)
B)
C)
D)

Question 30

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1500 pounds. At a 95% level, how many elephants need to be weighed so the average weight will be accurate to within 250 pounds?

A) 139
B) 165
C) 196
D) 324

Question 31

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Question 32

A study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 80% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 10 milligrams?

A) 225
B) 369
C) 613
D) 159

Question 33

The winning team's score in 7 high school basketball games was recorded. If the sample mean is 68.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.

A)
B)
C)
D)

Question 34

Identify the degree of confidence displayed in the confidence interval shown below.

A) 90%
B) 95%
C) 98%
D) 99%

Question 35

What is the value of $\alpha$ used in describing the confidence interval shown below.

A) 0.01
B) 0.02
C) 0.04
D) 0.05

Question 36

The t-distribution has a variance that is greater than one.

Question 37

The value of used in the figure below is 0.02.

Question 38

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A packer wishes to find the 90% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?

A) 25
B) 97
C) 69
D) 41

Question 39

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 20. If he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?

A) 45
B) 90
C) 180
D) 720

Question 40

3 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.

A)
B)
C)
D)

Question 41

A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 99% confidence?

A) 444
B) 888
C) 1776
D) 3552

Question 42

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?

A)
B)
C)
D)

Question 43

The rounding rule for a confidence interval for a proportion is to round off to three decimal places.

Question 44

A report states that 44% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3 percentage points with 92% confidence?

A) 247
B) 420
C) 545
D) 839

Question 45

A random sample of 70 printers discovered that 25 of them were being used in small businesses . Find the 95% limit for the population proportion of printers that are used in small businesses.

A) 0.150 < p < 0.564
B) 0.245 < p < 0.469
C) 0.263 < p < 0.452
D) 0.320 < p < 0.395

Question 46

The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary?

A) 966
B) 683
C) 1183
D) 484

Question 47

A retailer wants to estimate with 99% confidence the number of people who shop at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1,100.

Question 48

John Davis, a manager of a supermarket, wants to estimate the proportion of customers who use food stamps at his store. He has no initial estimate of what the sample proportion will be. How large a sample is required to estimate the true proportion to within 3 percentage points with 98% confidence?

A) 756
B) 1,849
C) 1,067
D) 1,509

Question 49

In a sample of 855 bartenders, 48.0% report hearing complaints from patrons about their jobs. If the margin of error for the proportion of bartenders hearing job complaints is 4.4 percentage points, what is the degree of confidence used?

A) 90%
B) 95%
C) 98%
D) 99%

Question 50

A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 99% confidence?

A) 153
B) 373
C) 457
D) 686

Question 51

The symbol for the sample proportion is ______.

Question 52

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?

A)
B)
C)
D)

Question 53

In a sample of 40 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less.

A) 35.6% < p < 48.4%
B) 32.0% < p < 52.0%
C) 29.1% < p < 54.9%
D) 22.7% < p < 61.3%

Question 54

A chi-square distribution is negatively skewed.

Question 55

A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective components to within 2.5 percentage points with 99% confidence?

Question 56

If is equal to 0.85, then is equal to ______.

A) 0.85
B) 0.50
C) 0.40
D) 0.15

Question 57

A sample of 400 racing cars showed that 80 of them cost over $700,000. What is the 99% confidence interval for the true proportion of racing cars that cost over $700,000?

Question 58

A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary?

A) 751
B) 1062
C) 33
D) 532

Question 59

The Pizza Shop wanted to determine what proportion of its customers ordered only cheese pizza. Out of 80 customers surveyed, 15 ordered only cheese pizza. What is the 99% confidence interval of the true proportion of customers who order only cheese pizza?

A)
B)
C)
D)

Question 60

A random sample of 100 voters found that 46% were going to vote for a certain candidate. Find the 95% limit for the population proportion of voters who will vote for that candidate.

A) 36.2% < p < 55.8%
B) 37.0% < p < 55.0%
C) 37.8% < p < 54.2%
D) 41.1% < p < 50.9%

Question 61

The value for for a 99% confidence interval when n = 24 is 9.262.

Question 62

A chi-square variable cannot be negative, and the distributions are positively skewed.

Question 63

The formula for the confidence interval for a standard deviation is ____________________.

Question 64

The area under each chi-square distribution is equal to _______.

Question 65

What is the value for for a 95% confidence interval when n = 18?

A) 7.564
B) 8.672
C) 9.390
D) 8.231

Question 66

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the population standard deviation in price with 90% confidence.

A)
B)
C)
D)

Question 67

Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 14.6 inches.

A)
B)
C)
D)

Question 68

What is the value for for a 98% confidence interval when n = 12?

A) 27.688
B) 24.725
C) 21.920
D) 26.217

Question 69

Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 11 trees has a standard deviation of 12.2 feet.

A) 11.2 < < 13.2
B) 8.5 < < 21.4
C) 137.8 < < 159.8
D) 72.7 < < 458.4

Question 70

What is the 95% confidence interval for the standard deviation of birth weights at County General Hospital, if the standard deviation of the last 25 babies born there was 1.1 pounds?

A)
B)
C)
D)

Question 71

For a random sample of 23 European countries, the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in all of Europe?

A)
B)
C)
D)

Question 72

In order to find confidence intervals for variances and standard deviations, one must assume that the variable is _________________.

Question 73

The value for for a 95% confidence interval when n = 15 is 26.119.

Question 74

Find the values for and when = .05 and n = 27.

A) 13.844 and 41.923
B) 14.573 and 43.194
C) 15.379 and 38.885
D) 16.151 and 40.113

Question 75

What is the 90% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam was 12.7?

A)
B)
C)
D)