Deck 7: Estimating Parameters and Determining Sample Sizes

Question 1

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

Answer 1

37.156

Question 2

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 population appears to be very skewed.

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

Answer 2

Neither the normal nor the t distribution applies.

Question 3

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)

Answer 3

Question 4

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

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

Question 5

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

A)
B)
C)
D)

Question 6

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

Question 7

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

Question 8

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 9

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 10

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 11

Use the given degree of confidence and sample data to construct a confidence interval for the

Question 12

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 13

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 14

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.
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.

A)
B)
C)
D)

Question 15

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

Question 16

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.

Question 17

Identify the distribution that applies to the following situation: In constructing a confidence interval of $\sigma$ 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 18

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 19

In constructing a confidence interval for a table is used to find the critical values
for values of For larger values of n ,
approximated by using the following formula:
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 20

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 21

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 22

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 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) p<0.062
B) p<0.154
C) p>0.062
D) p<0.167

Question 24

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

Question 25

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 26

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 27

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
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 28

Express the confidence interval 0.039

A)
B)
C)
D)

Question 29

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 30

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 31

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 32

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 33

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

A)
B)
C)
D)

Question 34

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 35

Find the degree of confidence used in constructing the confidence interval 0.523

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

Question 36

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) 0.405
B) 0.425
C) 0.426
D) 0.404

Question 37

4)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 38

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) 0.458
B) 0.461
C) 0.459
D) 0.463

Question 39

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 40

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) 20,308

Question 41

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 42

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

Question 43

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 44

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 45

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

Question 46

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 47

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 48

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 49

Under what circumstances can you replace with s in the formula

Question 50

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 51

Describe the steps for finding a confidence interval.

Question 52

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

Question 53

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

Question 54

Why is the best point estimate of ?

Question 55

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 56

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 57

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 58

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