Deck 7: Estimating Parameters and Determining Sample Sizes

Question 1

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

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

Answer 1

C

Question 2

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) 0.24
C) 0.50
D) 0.18

Answer 2

B

Question 3

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p .
n=195, x=162 ; 95 % confidence

A)
B)
C)
D)

Answer 3

Question 4

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)
B)
C)
D)

Question 5

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.
90% confidence interval for n=9 ; population appears to be very skewed.

A)
B)
C)
D) Neither the normal nor the t distribution applies.

Question 6

Express the confidence interval (0.432,0.52) in the form of

A)
B)
C)
D)

Question 7

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. n=30 , s=10.5,90 % confidence

A)
B)
C)
D)

Question 8

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

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

Question 9

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

A)
B)
C)
D)

Question 10

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) 0.0355
B) 0.0339
C) 0.0404
D) 0.0446

Question 11

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

Question 12

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 13

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.

A)
B)
C)
D)

Question 14

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.
95% confidence; n=2388, x=1672

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

Question 15

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

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

Question 16

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. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

A)
B)
C)
D)

Question 17

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.

Question 18

In constructing a confidence interval for or , a table is used to find the critical values for values of For larger values of n, can be
approximated by using the following formula: where k is the number of degrees of freedom and is the critical z-score. Construct the 90 % confidence interval for using the following sample data: a sample of size n=232 yields a mean weight of 154 lb and a standard deviation of 25.5 lb. Round the confidence interval limits to the nearest hundredth.

A)
B)
C)
D)

Question 19

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

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

Question 20

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

Question 21

A 99% confidence interval (in inches) for the mean height of a population is
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).

A)
B)
C)
D)

Question 22

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

A)
B)
C)
D)

Question 23

A one-sided confidence interval for p can be written as 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.

A)
B)
C)
D)

Question 24

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)
B)
C)
D)

Question 25

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n=130, x=69 ; 90% confidence

A)
B)
C)
D)

Question 26

Express the confidence interval in the form of

A)
B)
C)
D)

Question 27

You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

A) 57
B) 224
C) 14
D) 11

Question 28

Find the degree of confidence used in constructing the confidence interval - for the population proportion p using sample data with n=109, x=65 .

A) 88 %
B) 90 %
C) 95 %
D) 99 %

Question 29

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.

A)
B)
C)
D)

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

Question 31

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

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

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?

A)
B)
C)
D)

Question 33

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

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

Question 34

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)
B)
C)
D)

Question 35

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with
Construct a 95% confidence interval for the true mean cholesterol content, of all such eggs.

A)
B)
C)
D)

Question 36

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) 335
D) 250

Question 37

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 mg is 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) 99%
B) 95%
C) 98%
D) 80%

Question 38

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n=56, x=30 ; 95% confidence

A)
B)
C)
D)

Question 39

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

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

Question 40

Which of the following critical values is appropriate for a 98% confidence level where n=7 ; and the population appears to be normally distributed.

A)
B)
C)
D)

Question 41

The following is a 95 % confidence interval of the proportion of female medical school students: 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 42

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 43

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 44

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

Question 45

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

Question 46

Describe the process for finding the confidence interval for a population proportion

Question 47

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 48

Under what circumstances can you replace with s in the formula

Question 49

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 σ. Find
the minimum sample size. Is this sample size practical?

Question 50

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 51

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

Question 52

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 53

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

Question 54

Describe the steps for finding a confidence interval

Question 55

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 56

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

Question 57

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

Question 58

Why is the best point estimate of ?

Question 59

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

Question 60

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?