Deck 6: Confidence Intervals and Sample Size

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

A confidence interval was constructed around a proportion. The interval was from 13.5% to 21.5%. The
proportion that was used to construct this interval was 17.5%.

Question 5

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

Question 6

Only the degree of confidence and the maximum error are necessary to determine the sample size if one
uses the "conservative" value for the standard error.

Question 7

The width of a confidence interval for a population mean that is based on the t-distribution varies from
sample to sample even if the sample size and confidence level is kept fixed.

Question 8

According to Statistics Canada, on July 1, 2006 the population size of the province of Quebec was
7,651,531 whereas Nova Scotia was considerably smaller at 934,405. Thus the margin of error for a
Gallup Poll based on a random sample of 1000 Nova Scotians is smaller than that based on a random
sample of 1000 Quebeckers.

Question 9

A retailer wants to estimate with 99% confidence the number of people who buy 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

Question 10

A chi-square distribution is negatively skewed.

Question 11

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

Question 12

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

Question 13

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

Question 14

Noting that the critical z-value for a 95% confidence interval for a proportion is almost equal to 2, it
can be seen that the required sample size is approximately equal to the reciprocal of the squared desired
margin of error.

Question 15

Question 16

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
of 3.9 minutes. Jennifer's maximum error of estimate would be 1.4 minutes.

Question 17

The width of a confidence interval for a population variance is of constant width for fixed values of the
sample size and confidence level.

Question 18

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

Question 19

The (estimated) standard error of the mean is larger than the standard deviation of the sample from which
it was derived.

Question 20

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

Question 21

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

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

A) 0.321 < p < 0.379
B) 0.316 < p < 0.384
C) 0.309 < p < 0.391
D) 0.305 < p < 0.395

Question 23

If a population has standard deviation 18, what is the minimum sample size to be 95% confident that the error should be accurate to within 4?

A) 153
B) 9
C) 78
D) 18

Question 24

A researcher conducted a study of the access speed of 30 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
4, about how many hard drives should he include in his new sample?

A) 30
B) 60
C) 150
D) 750

Question 25

A study of elephants wishes to determine the average weight of a certain subspecies of elephants. The standard deviation of the population is 2000 pounds. How many elephants need to be weighed so find we
Can be 80% confident to be accurate within 300 pounds?

A) 73
B) 94
C) 121
D) 400

Question 26

A previous 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 99% confidence interval for the average
Weight of a nickel. How many nickels does he need to weigh to be accurate within 15 milligrams?

A) 100
B) 666
C) 955
D) 542

Question 27

A study of peach trees showed that the average number of peaches per tree was 1000. The standard deviation of the population is 150. A scientist wishes to find the 98% confidence interval for the mean
Number of peaches per tree. How many trees does she need to sample to be accurate within 20 peaches
Per tree?

A) 57
B) 217
C) 257
D) 306

Question 28

A study of 60 professors showed that the time they spent on the average in creating test questions was 17.0 minutes per question. The standard deviation of the population is 2. Which of the following is the 98% confidence interval for the average number of minutes it takes to create a test question?

A) (15.99, 18.01)
B) (16.58, 17.42)
C) (16.40, 17.60)
D) (12.35, 21.65)

Question 29

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 7 millimeters. A pakcer 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) 6
B) 21
C) 15
D) 9

Question 30

A study of 90 bolts of carpet showed that their average length was 180 yards. The standard deviation of the population is 10 yards. Which of the following is the 99% confidence interval for the mean length per
Bolt of carpet?

A) (177.55, 182.45)
B) (173.49, 186.51)
C) (176.74, 183.26)
D) (177.28, 182.72)

Question 31

In 2000 there were almost 300,000 Canadians with more than 1 million dollars in financial assets! If the average age of one hundred randomly selected millionaires was 54.8 years with a standard deviation of 7.9 years, what is the 95% confidence interval for the mean age, of all Canadian millionaires?

Question 32

A lawyer researched the average number of years served by 45 different judges on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the
95% confidence interval for the average number of years served by all Supreme Court judges?

Question 33

A food snack manufacturer samples 9 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 9.6 and the sample standard deviation is 0.20, find the 95% confidence interval of the

A) (9.53, 9.67)
B) (9.14, 10.06)
C) (9.47, 9.73)
D) (9.45, 9.75)

Question 34

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

Question 35

A study of 100 apple trees showed that the average number of apples per tree was 2000. The standard deviation of the population is 150. Which of the following is the 95% confidence interval for the mean
Number of apples for all trees?

A) (1975.3, 2024.7)
B) (1970.6, 2029.4)
C) (1967.7, 2032.3)
D) (1965.1, 2034.9)

Question 36

The winning team's scores in 9 high school basketball games were recorded. If the sample mean is 10.5 points and the sample standard deviation is 0.15 points, find the 98% confidence interval of the

A) (10.45, 10.55)
B) (10.36, 10.64)
C) (10.38, 10.62)
D) (10.21, 10.79)

Question 37

8 squirrels were found to have an average weight of 10.5 ounces with a sample standard deviation is 0.30. Find the 95% confidence interval of the

A) (10.25, 10.75)
B) (9.53, 11.47)
C) (10.23, 10.77)
D) (10.39, 10.61)

Question 38

A study of 60 white mice showed that their average weight was 5.7 ounces. The standard deviation of the population is 0.4 ounces. Which of the following is the 90% confidence interval for the mean weight per
White mouse?

A) (5.62, 5.78)
B) (5.50, 5.90)
C) (5.60, 5.80)
D) (5.04, 6.36)

Question 39

A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year. Assume a population standard deviation of 23.8 days. What is the 90% confidence interval for the
Average days worked, of all payroll departments?

Question 40

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

Question 41

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

A) 0.075 < p < 0.300
B) 0.115 < p < 0.260
C) 0.086 < p < 0.289
D) 0.102 < p < 0.273

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

A) 0.620 < p < 0.780
B) 0.591 < p < 0.812
C) 0.584 < p < 0.830
D) 0.615 < p < 0.805

Question 43

A report states that 46% of home owners had a vegetable garden. How large a sample is needed to estimate the

A) 96
B) 191
C) 382
D) 764

Question 44

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?

Question 45

A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the

A) 107
B) 181
C) 213
D) 362

Question 46

A) 0.76
B) 0.50
C) 0.42
D) 0.24

Question 47

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

A) 23.053
B) 24.725
C) 25.090
D) 24.278

Question 48

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% of the

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

Question 49

A random sample of 95 printers discovered that 25 of them were being used in small businesses. Find the 99% limit for the population proportion of printers that are used in small businesses.

A) 0.042 < p < 0.485
B) 0.147 < p < 0.380
C) 0.158 < p < 0.368
D) 0.224 < p < 0.302

Question 50

John Davis, a manager of a supermarket, wants to estimate the proportion of customers that will be using discount coupons at his store. How large a sample is required to estimate the

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

Question 51

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

A) 0.148 < p < 0.192
B) 0.136 < p < 0.204
C) 0.144 < p < 0.196
D) 0.139 < p < 0.201

Question 52

A sample of 1,108 was used to estimate a proportion with 98% confidence. If p = 0.5, what was the amount of error?

A) 0.040
B) 0.025
C) 0.035
D) 0.028

Question 53

In a sample of 855 bartenders, 48% heard complaints from patrons about work. If the margin of error was 4.4%, what was the confidence level that was used?

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

Question 54

In a sample of 50 mice, a biologist found that 38% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run that maze in 30 seconds or less.

Question 55

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

Question 56

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

A) 7.564
B) 7.289
C) 6.547
D) 8.312

Question 57

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

A) 751
B) 1062
C) 1301
D) 532

Question 58

Question 59

A random sample of 80 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) 35.1% < p < 56.9%
B) 36.0% < p < 56.0%
C) 36.8% < p < 55.2%
D) 40.5% < p < 51.5%

Question 60

A college believes that 28% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the

A) 287
B) 861
C) 1292
D) 1464

Question 61

The average number of miles that 90 truckers drove in a day was 540 with a standard deviation of 40
miles. What is the 99% confidence interval of the

Question 62

A sample of 23 European countries found that the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in Europe?

Question 63

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

Question 64

In a study of size 8 where the variance is unknown, the distribution that should be used to calculate confidence intervals is

A) a 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 65

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

Question 66

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

Question 67

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

Question 68

Using Table G, find the values for and for

A) 15.379 and 38.885
B) 16.151 and 40.113
C) 16.5395 and 40.725
D) 16.928 and 41.337

Question 69

The symbol for the sample proportion is __________.
________________________________________

Question 70

Find the 95% confidence interval for the variance of the lengths of pipes if a sample of 16 pipes has a standard deviation of 12 inches.

Question 71

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

Question 72

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

Question 73

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

Question 74

Question 75

Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 12 trees has a standard deviation of 10 feet.

Question 76

A 90% confidence interval around the variance was calculated. For n = 27, the confidence interval was 35.0-88.4. Give the variance of the sample.