Deck 7: Confidence Intervals and Sample Size

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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 true proportion.The minimum sample size necessary would be 1,100.

Question 7

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 8

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

Question 9

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

Question 10

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 11

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 12

A chi-square distribution is negatively skewed.

Question 13

The value of used in the figure below is 0.025.

Question 14

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

Question 15

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 16

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

Question 17

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

Question 18

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 19

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 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

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 22

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 23

Find the value of  as shown in the figure below.

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

Question 24

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
True mean.

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

Question 25

Identify the confidence interval used in the figure below.

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

Question 26

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?

A)
B)
C)
D)

Question 27

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, μ, of all Canadian millionaires?

A)
B)
C)
D)

Question 28

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 29

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 30

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 31

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 32

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 33

The term refers to the

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

Question 34

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 35

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 36

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 true mean weight.

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

Question 37

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 true
Mean.

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

Question 38

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 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, μ, of all payroll departments?

A)
B)
C)
D)

Question 40

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 41

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 42

A report states that 46% 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 5% with 95%
Confidence?

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

Question 43

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?

A)
B)
C)
D)

Question 44

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 45

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 46

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.

A)31.3% < p < 44.7%
B)26.7% < p < 49.3%
C)24.5% < p < 51.5%
D)17.8% < p < 58.2%

Question 47

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 48

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 49

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 50

If is equal to 0.76, then is equal to

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

Question 51

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 6% with 98%
Confidence?

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

Question 52

A college believes that 28% 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 3% with 95% confidence?

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

Question 53

In a study of 100 new cars, 29 of them were white.Find and where is the proportion of new cars that is white.

A) = 0.29,0.29
B) 0.29, = 0.71
C) = 0.71,0.29
D) 0.71, = 0.71

Question 54

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 55

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 true proportion to within 3%
With 98% confidence?

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

Question 56

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

Question 57

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 true
Proportion of customers who order only cheese pizza?

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 58

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)

Question 59

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 true proportion.
How large a sample is necessary?

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

Question 60

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?

A)
B)
C)
D)

Question 61

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

Question 62

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

Question 63

One of the characteristics of the t-distribution is that the curve never touches the __________.
________________________________________

Question 64

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.

A)
B)
C)
D)

Question 65

The symbol for the sample proportion is __________.
________________________________________

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 true proportion of defective components with
99% confidence? (Using the text z-table value)

Question 67

The average number of mosquitos caught by 64 mosquito traps was 900 with a standard deviation of 100.
What is the 99% confidence interval for the true mean number of mosquitos caught by all mosquito traps?

Question 68

The formula for the confidence interval for a standard deviation is __________.
________________________________________

Question 69

Using Table G, find the values for and for = 05 and n = 27.

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 70

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

Question 71

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.

A)
B)
C)
D)

Question 72

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

Question 73

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

Question 74

Which value of was used in the figure below?