Deck 7: Estimating Parameters and Determining Sample Sizes

Question 1

Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution.

Answer 1

C

Question 2

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A) 0.789 < p < 0.873
B) 0.778 < p < 0.883
C) 0.788 < p < 0.873
D) 0.777 < p < 0.884

Answer 2

B

Question 3

Answer 3

C

Question 4

Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over six feet tall. What is the best point estimate of the proportion of people in the population who are over 6
Feet tall?

A) 0.76
B) 0.18
C) 0.24
D) 0.50

Question 5

Find the critical value corresponding to a sample size of 19 and a confidence level of 99 percent.

A) 34.805
B) 6.265
C) 7.015
D) 37.156

Question 6

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s =
17)6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Question 7

Find the value of that corresponds to a confidence level of 89.48%.

A) 1.25
B) 1.62
C) -1.62
D) 0.0526

Question 8

If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n ________ (up or down) to the next ________ (smaller or larger) whole number.

A) up; smaller
B) down; larger
C) up; larger
D) down; smaller

Question 9

Find the critical value that corresponds to a 91% confidence level.

A) 1.34
B) 1.75
C) 1.645
D) 1.70

Question 10

Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.

A) 0.0251 < p < 0.0854
B) 0.0360 < p < 0.0745
C) 0.0280 < p < 0.0826
D) 0.0323 < p < 0.0782

Question 11

Do one of the following, as appropriate: (a) Find the critical value , (b) find the critical value , (c) state that neither the normal nor the t distribution applies.

Question 12

A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union
Members who favor the Republican candidate.

Question 13

Identify the distribution that applies to the following situation: In constructing a confidence interval ofσ you have 50 sample values and they appear to be from a population with
A skewed distribution.

A) Normal distribution
B) Student t distribution
C) Chi-square distribution
D) None of the three distributions is appropriate.

Question 14

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%;

A) 1116
B) 2223
C) 2115
D) 1939

Question 15

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6,
Construct a 99% confidence interval for the mean score of all students.

Question 16

Question 17

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

A) 0.0206
B) 0.0184
C) 0.0156
D) 0.0248

Question 18

Which critical value is appropriate for a 99% confidence level where n = 17; is unknown and the population appears to be normally distributed?

Question 19

The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.

A) increases; decreases
B) decreases; decreases
C) decreases; increases
D) increases; increases

Question 20

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.
98% confidence; the sample size is 800, of which 40% are successes

A) 0.0339
B) 0.0446
C) 0.0355
D) 0.0404

Question 21

To be able to say with 95% confidence that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what
Quantity?

A) 805
B) 192
C) 250
D) 335

Question 22

A one-sided confidence interval for p can be written as E where the margin of error E is modified by replacing with . If a teacher wants to report that the fail rate on a test is at most x with 90%
Confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of
74 students results in 8 who fail the test.

Question 23

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.008; confidence level: 98%;

A) 20,308
B) 21,207
C) 10,384
D) 22,184

Question 24

Which of the following critical values is appropriate for a 98% confidence level where nd the population appears to be normally distributed.

Question 25

Do one of the following, as appropriate: (a) Find the critical value , (b) find the critical value 99%; n = 17; is unknown; population appears to be normally distributed.

A) zσ/2 = 2.583
B) tσ/2 = 2.921
C) tσ/2 = 2.898
D) zσ/2 = 2.567

Question 26

Question 27

A 99% confidence interval (in inches) for the mean height of a populatio This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample
Mean and sample standard deviation).

Question 28

To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval
For the population standard deviation

Question 29

Question 30

Identify the distribution that applies to the following situation: In constructing a confidence interval of , you have 50 sample values and they appear to be from a population
With a skewed distribution. The population standard deviation is not known.

A) Normal distribution
B) Student t distribution
C) Chi-square distribution
D) None of the three distributions is appropriate.

Question 31

Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s =
17)6 milligrams. A confidence interval of constructed for the true mean cholesterol
Content of all such eggs. It was assumed that the population has a normal distribution. What confidence level
Does this interval represent?

A) 98%
B) 99%
C) 80%
D) 95%

Question 32

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, , of all students taking the test?

Question 33

Question 34

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

Question 35

Express a confidence interval defined as (0.432, 0.52) in the form of the point estimate ________ ± the margin of error ________. Express both in three decimal places.

A) 0.432; 0.088
B) 0.432; 0.044
C) 0.476; 0.088
D) 0.476; 0.044

Question 36

Express the confidence interval 0

Question 37

Question 38

Fill in the blank: The critical value that corresponds to a ________% confidence level is 2.33.

A) 88
B) 90
C) 99
D) 98

Question 39

Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

Question 40

Find the critical value corresponding to a sample size of 19 and a confidence level of 99 percent.

A) 34.805
B) 6.265
C) 7.015
D) 37.156

Question 41

Interpret the following 95% confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta.

Question 42

The following is a 95% confidence interval of the proportion of female medical school students: 0.449 < p <
0.511, based on data from the American Medical Association. What is the point estimate of the proportion of
females in the population of medical school students? Write a brief statement that correctly interprets the
confidence interval given.

Question 43

Find the critical value that corresponds to a 98% confidence level.

A) 2.33
B) 2.575
C) 1.75
D) 2.05

Question 44

Six human skulls from around 4000 B.C. were measured, and the lengths have a mean of 94.2 mm and a
standard deviation of 4.9 mm. If you want to construct a 95% confidence interval estimate of the mean length of
skulls, what requirements must be satisfied?

Question 45

Identify the correct distribution (z, t, or neither) for each of the following.

Question 46

?

Question 47

Define in as clear language as possible how a 95% confidence interval can be used for hypothesis tests.

Question 48

In a Gallup poll of 557 randomly selected adults, 284 said that they were underpaid. Identify the best point
estimate of the percentage of adults who say they are underpaid. Construct a 95% confidence interval estimate
of the percentage of adults who say that that they are underpaid. Can we safely conclude that the majority of
adults say that they are underpaid?

Question 49

Under what circumstances can you replace σ with s in the formula ?

Question 50

Draw a diagram of the chi-square distribution. Discuss its shape and values.

Question 51

Define margin of error. Explain the relation between the confidence interval and the margin of error. Suppose a
confidence interval i . Redefine the confidence interval into a format using the margin of error
and the point estimate of the population mean.

Question 52

Based on a simple random sample of students from her school, Sally obtained a point estimate of the mean
weight of students at her school. What additional information would be provided by a confidence interval
estimate of the mean weight?

Question 53

In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages and 64% of them said that they
did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic
beverages. Can we safely conclude that the majority of adults consume alcoholic beverages?

Question 54

Bert constructed a confidence interval to estimate the mean weight of students in his class. The population was
very small - only 30. Ruth constructed a confidence interval for the mean weight of all adult males in the city.
She based her confidence interval on a very small sample of only 5. Which confidence interval is likely to give a
better estimate of the mean it is estimating? Which is likely to be more of a problem, a small sample or a small
population?

Question 55

How do you determine whether to use the z or t distribution in computing the margin of error,

Question 56

You want to estimateσ for the population of waiting times at McDonald's drive-up windows, and you want to
be 95% confident that the sample standard deviation is with 20% of Find the minimum sample size. Is this
sample size practical?

Question 57

In general, what does "degrees of freedom" refer to? Find the degrees of freedom for the given information,
assuming that you want to construct a confidence interval estimate of Six human skulls from around 4000
B.C. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9 mm.

Question 58

In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages and 64% of them said that they
did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic
beverages. Can we safely conclude that the majority of adults consume alcoholic beverages?

Question 59

When determining the sample size needed to achieve a particular error estimate you need to know σ. What are
two methods of estimating σ if σ is unknown?

Question 60

Describe the steps for finding a confidence interval.

Question 61

Express the confidence interval using the indicated format.

Question 62

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
90% confidence; n = 300, x = 140

A) 0.0593
B) 0.0474
C) 0.0509
D) 0.0565

Question 63

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
95% confidence; n = 380, x = 50

A) 0.0306
B) 0.0408
C) 0.0340
D) 0.0357

Question 64

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
90% confidence; the sample size is 1510, of which 35% are successes

A) 0.0241
B) 0.0252
C) 0.0202
D) 0.0157

Question 65

Express the confidence interval using the indicated format.

Question 66

Find the critical value that corresponds to a 91% confidence level.

A) 1.34
B) 1.75
C) 1.70
D) 1.645

Question 67

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
95% confidence; n = 2388, x = 1672

A) 0.0156
B) 0.0206
C) 0.0248
D) 0.0184

Question 68

Solve the problem.

A) 0.724
B) 0.688
C) 0.708
D) 0.706

Question 69

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
99% confidence; the sample size is 1110, of which 45% are successes

A) 0.0293
B) 0.0385
C) 0.0306
D) 0.0348

Question 70

Find the value of that corresponds to a confidence level of 89.48%.

A) 1.25
B) -1.62
C) 0.0526
D) 1.62

Question 71

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
99% confidence; n = 5900, x = 1770

A) 0.0117
B) 0.0135
C) 0.0154
D) 0.00878

Question 72

Find the critical value that corresponds to a 93% confidence level.

A) 2.70
B) 1.48
C) 1.81
D) 1.96

Question 73

Solve the problem.
The following confidence interval is obtained for a population proportion, p: (0.399, 0.437). Use these confidence interval limits to find the margin of error, E.

A) 0.020
B) 0.017
C) 0.019
D) 0.038

Question 74

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
98% confidence; the sample size is 800, of which 40% are successes

A) 0.0339
B) 0.0446
C) 0.0355
D) 0.0404

Question 75

Solve the problem.
The following confidence interval is obtained for a population proportion, p: 0.724 < p < 0.752. Use these confidence interval limits to find the margin of error, E.

A) 0.028
B) 0.738
C) 0.014
D) 0.015

Question 76

Solve the problem.
The following confidence interval is obtained for a population proportion, p: 0.753 < p < 0.797. Use these confidence interval limits to find the point estimate,

A) 0.775
B) 0.753
C) 0.780
D) 0.770

Question 77

Find

A) 1.48
B) 1.96
C) 2.70
D) 1.81

Question 78

Express the confidence interval using the indicated format.

Question 79

Express the confidence interval using the indicated format.

Question 80

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
95% confidence; the sample size is 9900, of which 30% are successes

A) 0.0104
B) 0.00677
C) 0.0119
D) 0.00903