Deck 7: Confidence Intervals and Sample Size

Question 1

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

Answer 1

maximum error of estimate

Question 2

Answer 2

A

Question 3

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

Answer 3

Question 4

A) 0.60
B) 3.26
C) 0.56
D) 1.18

Question 5

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 6

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

Question 7

A) 3.71
B) 2.58
C) 2.81
D) 2.53

Question 8

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

Question 9

Question 10

Question 11

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.

Question 13

The average number of mosquitos caught in 64 mosquito traps in a particular
environment was 700 per trap. The standard deviation of mosquitos caught in the
entire population of traps is 100 mosquitos. What is the 99% confidence interval
for the true mean number of mosquitos caught in all mosquito traps?

Question 14

Question 15

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.

Question 16

owing

A) (139.7, 148.8)
B) (136.9, 151.6)
C) (124.6, 163.8)
D) (85.4, 203.0

Question 17

A) 1.25
B) 0.97
C) 0.81
D) 1.98

Question 18

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 19

Find the level of the confidence interval that has the given critical value. 2.16

A) 98.46%
B) 96.92%
C) 3.08%
D) 1.54%

Question 20

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

Question 21

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 13 millimeters. A packer wishes to find the 95% confidence interval for the
Average length of a box. How many boxes does he need to measure to be accurate within
4 millimeters?

A) 29
B) 58
C) 41
D) 11

Question 22

The three confidence intervals below were constructed from the same sample. One of them was computed at a confidence level of 90%, another at a confidence level of 95%, and another at a
Confidence level of 98%.
Which is the confidence level at 98%?

Question 23

A) The likelihood cannot be determined.
B) Yes
C) No

Question 24

A) 215
B) 118
C) 7
D) 11

Question 25

A study of nickels showed that the the standard deviation of the weight of nickels is milligrams. A coin counter manufacturer wishes to find the 95% confidence interval for
The average weight of a nickel. How many nickels does he need to weigh to obtain an
Average accurate to within 20 milligrams?

A) 154
B) 57
C) 217
D) 306

Question 26

Question 27

A) 117
B) 5
C) 6
D) 34

Question 28

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 500 pounds. At a
90% level, how many elephants need to be weighed so the average weight will be
Accurate to within 250 pounds?

A) 16
B) 11
C) 13
D) 36

Question 29

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 24. If he were to conduct a second study to reduce
The maximum error of estimate to 6, about how many hard drives should he include in his
New sample?

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

Question 30

A study of 95 apple trees showed that the average number of apples per tree was 525 The standard deviation of the population is 200. Which of the following is the 80%
Confidence interval for the mean number of apples per tree for all trees?

Question 31

A) None of these are true.
B) The probability that the population mean is between 593.8 hours and 604.2 hours is 0.95.
C) 95% of the light bulbs in the sample had lifetimes between 593.8 hours and 604.2 hours
D) We are 95% confident that the mean lifetime of all the bulbs in the population is between 593.8 hours and 604.2 hours.

Question 32

A study of 40 white mice showed that their average weight was 3.20 ounces. The standard deviation of the population is 0.8 ounces. Which of the following is the 80%
Confidence interval for the mean weight per white mouse?

Question 33

A study of 55 professors showed that the average time they spent creating test questions was 16.5 minutes per question. The standard deviation of the population is 5.8. Which
Of the following is the 99% confidence interval for the average number of minutes it
Takes to create a test question?

Question 34

Question 35

If a population has a standard deviation of 14, 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 5 of the true mean?

A) 61
B) 12
C) 31
D) 6

Question 36

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

Question 37

A study of peach trees found that the average number of peaches per tree was 1025. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the
99% 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 18 peaches per tree?

A) 23
B) 26
C) 21
D) 4

Question 38

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

Question 39

_ and

A) 95%, 29.856, 39.608
B) 5%, 0, 34.732
C) 95%, 0, 34.732
D) 5%, 29.856, 39.608

Question 40

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 41

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

Question 42

_ and

A) 5%, 0, 49.304
B) 95%, 0, 49.304
C) 5%, 46.915, 51.693
D) 95%, 46.915, 51.693

Question 43

Question 44

A) 1.960
B) 2.228
C) 1.812
D) 2.201

Question 45

Question 46

Question 47

A) (30.461, 33.137)
B) (28.581, 35.017)
C) (27.980, 35.618)
D) (27.570, 36.028)

Question 48

rror of

A) 511
B) 18
C) 416
D) 296

Question 49

A) 1.721
B) 1.645
C) 1.725
D) 1.325

Question 50

Question 51

Question 52

rror of

A) 284
B) 15
C) 348
D) 202

Question 53

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.
121 125 151 129
127 133 121 125

Question 54

A sample of 125 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with
10 corresponding to "completely effective" and 1 corresponding to "completely
Ineffective". The average rating was 4.1 and the standard deviation was 4.0.
Construct a 95% confidence interval for the mean score.

Question 55

A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is
0)50 oz., find the 95% confidence interval of the true mean.

Question 56

)

A) The likelihood cannot be determined.
B) No
C) Yes

Question 57

Question 58

A) 2.20
B) 1.52
C) 1.80
D) 2.92

Question 59

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

Question 60

)

Question 61

7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.

Question 62

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?

Question 63

A) 125
B) 0.483
C) 0.031
D) 0.517

Question 64

A) 3.9856
B) 72
C) 73
D) 71

Question 65

A) 2.462
B) 2.750
C) 2.760
D) 2.457

Question 66

A) (92.161, 124.093)
B) (105.235, 111.018)
C) (93.878, 122.376)
D) (105.546, 110.707)

Question 67

In a survey of 246 registered voters, 132 of them wished to see Mayor Waffleskate lose her next election. Find a point estimate for the proportion of registered voters who wish
To see Mayor Waffleskate defeated.

A) 0.463
B) 132
C) 0.032
D) 0.537

Question 68

A) 0.428
B) 0.572
C) r0.036
D) 0.093

Question 69

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 70

In a survey of 305 registered voters, 130 of them wished to see Mayor Waffleskate lose her next election. Construct a 95% confidence interval for the proportion of registered
Voter who want to see Mayor Waffleskate defeated.

Question 71

In a sample of 45 mice, a biologist found that 40% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run a maze in
30 seconds or less.

Question 72

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?

Question 73

Question 74

A random sample of 50 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.

Question 75

A) 0.607
B) 0.034
C) 122
D) 0.393

Question 76

Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.

A) 5%, 57.84, 60.48
B) 95%, 0, 59.158
C) 5%, 0, 59.158
D) 95%, 57.84, 60.48

Question 77

Question 78

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?

Question 79

In a survey of 445 registered voters, 131 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 30% of registered
Voters wish to see her defeated. Does the 98% confidence interval for the proportion
Support this claim? (Hint: you should first construct the 98% confidence interval for the
Proportion of registered voters who whish to see Waffleskate defeated.)
(0)244, 0.345)

A) Yes
B) No
C) The reasonableness of the claim cannot be determined.

Question 80

The winning team's score in 13 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 13.0 points, find the
98% confidence interval of the true mean.