Deck 8: Confidence Interval Estimation

Question 1

The general form of a confidence interval is:

A)Point Estimate = Multiple × Standard Error
B)Point Estimate = Multiple +Standard Error
C)Point Estimate ± Multiple × Standard Error
D)Point Estimate = Multiple ± Standard Error

Answer 1

C

Question 2

If you increase the confidence level,the confidence interval _____.

A)decreases
B)increases
C)stays the same
D)may increase or decrease,depending on the sample data

Answer 2

B

Question 3

Suppose there are 500 accounts in a population.You sample 50 of them and find a sample mean of $500.What would be your estimate for the population total?

A)$5,000
B)$50,000
C)$250,000
D)$500,000
E)None of the above

Answer 3

C

Question 4

Two independent samples of sizes 20 and 25 are randomly selected from two normal populations with equal variances.In order to test the difference between the population means,the test statistic is:

A)a standard normal random variable
B)approximately standard normal random variable
C)t-distributed with 45 degrees of freedom
D)t-distributed with 43 degrees of freedom

Question 5

When you calculate the sample size for a proportion,you use an estimate for the population proportion; namely .A conservative value for n can be obtained by using = _____.

A)0.01
B)0.05
C)0.10
D)0.50
E)1.00

Question 6

The t-distribution for developing a confidence interval for a mean has _____ degrees of freedom.

A)n + 2
B)n +1
C)n
D)n - 1
E)n - 2

Question 7

If you are constructing a confidence interval for a single mean,the confidence interval will _____ with an increase in the sample size.

A)decrease
B)increase
C)stay the same
D)increase or decrease,depending on the sample data

Question 8

Confidence intervals are a function of which of the following three things?

A)The population,the sample,and the standard deviation
B)The sample,the variable of interest,and the degrees of freedom
C)The data in the sample,the confidence level,and the sample size
D)The sampling distribution,the confidence level,and the degrees of freedom
E)The mean,median,and mode

Question 9

After calculating the sample size needed to estimate a population proportion to within 0.05,you have been told that the maximum allowable error (B)must be reduced to just 0.025.If the original calculation led to a sample size of 1000,the sample size will now have to be:

A)2000
B)4000
C)1000
D)8000

Question 10

As the sample size increases,the t-distribution becomes more similar to the ________ distribution.

A)normal
B)exponential
C)multinominal
D)chi-square
E)binomial

Question 11

When we replace with the sample standard deviation (s),we introduce a new source of variability and the sampling distribution becomes the _____.

A)t -distribution
B)F- distribution
C)chi-square distribution
D)normal distribution

Question 12

The number of degrees of freedom needed to construct 90% confidence interval for the difference between means when the data are gathered from paired samples,with 15 observations in each sample,is:

A)30
B)15
C)28
D)14

Question 13

When the samples we want to compare are paired in some natural way,such as pretest/posttest for each person or husband/wife pairs,a more appropriate form of analysis is to not compare two separate variables,but their _____.

A)difference
B)sum
C)ratio
D)total
E)product

Question 14

If the odds of a horse winning a race are 2 to 1,then the probability of this horse winning the race is_____.

A)1/4
B)1/3
C)1/2
D)2/3
E)None of the above

Question 15

There are,generally speaking,two types of statistical inference.They are:

A)sample estimation and population estimation
B)confidence interval estimation and hypothesis testing
C)interval estimation for a mean and point estimation for a proportion
D)independent sample estimation and dependent sample estimation
E)None of the above

Question 16

From a sample of 500 items,30 were found to be defective.The point estimate of the population proportion defective will be:

A)0.06
B)30.0
C)16.667
D)None of the above

Question 17

Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means, .The sampling distribution of the sample mean difference is:

A)normally distributed
B)approximately normal
C)t - distributed with 98 degrees of freedom
D)chi-squared distributed with 99 degrees of freedom

Question 18

The approximate standard error of the point estimate of the population total is:

A)
B)
C)
D)

Question 19

A parameter such as is sometimes referred to as a ________ parameter,because many times we need its value even though it is not the parameter of primary interest.

A)special
B)random
C)nuisance
D)independent
E)dependent

Question 20

The chi-square and F-distributions are used primarily to make inferences about population ___________.

A)means
B)variances
C)medians
D)modes
E)proportions

Question 21

The lower limit of the 95% confidence interval for the population proportion p,given that n = 300; and = 0.10 is 0.1339.

Question 22

A 90% confidence interval estimate for a population mean is determined to be 72.8 to 79.6.If the confidence level is reduced to 80%,the confidence interval for becomes narrower.

Question 23

In general,the paired-sample procedure is appropriate when the samples are naturally paired in some way and there is a reasonably large positive correlation between the pairs.In this case,the paired-sample procedure makes more efficient use of the data and generally results in narrower confidence intervals.

Question 24

If the standard error of the sampling distribution of the sample proportion is 0.0324 for samples of size 200,then the population proportion must be 0.30.

Question 25

The chi-square distribution for developing a confidence interval for a standard deviation has_____ degrees of freedom.

A)n + 2
B)n +1
C)n
D)n - 1
E)n - 2

Question 26

An example of a problem where the sample data would be paired is:

A)Difference between the means of appraised and sales house prices
B)Difference between the proportion of defective items from two suppliers
C)Difference in the mean life of two major brands of batteries
D)Difference in the mean salaries for graduates in two different academic fields at a university
E)None of these options

Question 27

The 95% confidence interval for the population mean ,given that the sample size n = 49 and the population standard deviation = 7,is .

Question 28

The interval estimate 18.5 2.5 was developed for a population mean when the sample standard deviation s was 7.5.Had s equaled 15,the interval estimate would be 37 5.0.

Question 29

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual true value of the population parameter will fall within the interval.

Question 30

The shape of a chi-square distribution

A)is symmetric
B)is skewed to the left
C)is skewed to the right
D)depends on the sample data

Question 31

In developing a confidence interval for the population standard deviation ,we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution,but rather a right-skewed distribution called the chi-square distribution,which (for this procedure)has n - 1 degrees of freedom.

Question 32

If two random samples of sizes 30 and 35 are selected independently from two populations whose means are 85 and 90,then the mean of the sampling distribution of the sample mean difference, ,equals 5.

Question 33

For a given confidence level,the procedure for controlling interval length usually begins with the specification of

A)the point estimate
B)the population standard deviation,s
C)the sample standard deviation,s
D)the interval half-length,B

Question 34

The degrees of freedom for the t and chi-square distributions is a numerical parameter of the distribution that defines the precise shape of the distribution.

Question 35

In order to construct a confidence interval estimate of the population mean ,the value of must be given.

Question 36

The standard error of the sampling distribution of the sample proportion ,when the sample size n = 50 and the population proportion p = 0.25,is 0.00375.

Question 37

If a random sample of size 250 is taken from a population,where it is known that the population proportion p = 0.4,then the mean of the sampling distribution of the sample proportion is 0.60.

Question 38

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size n is greater than 30.

Question 39

We can form a confidence interval for the population total T by finding a confidence interval for the population mean in the usual way,and then multiplying the lower and upper limits the confidence interval by the population size N.

Question 40

If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference, ,equals 1.4142.

Question 41

The approximate standard error of the point estimate of the population total is .

Question 42

(A)Construct a 99% confidence interval for the proportion of company employees who prefer plan A.Assume that the population consists of the preferences of all employees in the frame.
(B)Interpret the 99% confidence interval constructed in (A).

Question 43

If we cannot make the strong assumption that the variances of two samples are equal,then we must use the pooled standard deviation in calculating the standard error of a difference between the means.

Question 44

You have been assigned to determine whether more people prefer Coke to Pepsi.Assume that roughly half the population prefers Coke and half prefers Pepsi.How large a sample would you need to take to ensure that you could estimate,with 95% confidence,the proportion of people preferring Coke within 3% of the actual value?

Question 45

(A)Compute a 95% confidence interval for the true proportion of people who favor Coke.Do the results of this poll convince you that a majority of people favors Coke?
(B)Suppose 2,000 (not 400)people were polled and 53% favored Coke.Would you now be convinced that a majority of people favor Coke? Why might your answer be different than in (A)?
(C)How many people would have to be surveyed to be 95% confident that you can estimate the fraction of people who favor Coca-Cola within 1%?

Question 46

The t-distribution and the standard normal distribution are practically indistinguishable as the degrees of freedom increase.

Question 47

If two samples contain the same number of observations,then the data must be paired.

Question 48

Samples of exam scores for employees before and after a training class would be examples of paired data

Question 49

In developing confidence interval for the difference between two population means using two independent samples,we use the pooled estimate in estimating the standard error of the sampling distribution of the sample mean difference if the populations are normal with equal variances.

Question 50

In determining the sample size n for estimating the population proportion p,a conservative value of n can be obtained by using 0.50 as an estimate of p.

Question 51

In general,increasing the confidence level will narrow the confidence interval,and decreasing the confidence level widens the interval.

Question 52

If a sample has 20 observations and a 95% confidence estimate for is needed,the appropriate value of t-multiple is 2.093

Question 53

You are told that a random sample of 150 people from Iowa has been given cholesterol tests,and 60 of these people had levels over the "safe" count of 200.Construct a 95% confidence interval for the population proportion of people in Iowa with cholesterol levels over 200.

Question 54

You are trying to estimate the average amount a family spends on food during a year.In the past,the standard deviation of the amount a family has spent on food during a year has been approximately $1200.If you want to be 99% sure that you have estimated average family food expenditures within $60,how many families do you need to survey?

Question 55

The mean of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.15,is 15.0.

Question 56

(A)Use a t - value of 2.014 to calculate a 95% confidence interval for the difference between the average female purchase and the average male purchase.Would you conclude that there is a significant difference between females and males in this case? Explain.
(B)What are the degrees of freedom for the t-multiple in this calculation? Explain how you would calculate the degrees of freedom in this case.
(C)What is the assumption in this case that allows you to use the pooled standard deviation for this confidence interval?

Question 57

The confidence interval for the population standard deviation s is centered at the point estimate,the sample standard deviation s.

Question 58

When samples of size n are drawn from a population,then the sampling distribution of the sample mean is approximately normal,provided that n is reasonably large.

Question 59

The upper limit of the 90% confidence interval for the population proportion p,given that n = 100; and = 0.20 is 0.2658.

Question 60

(A)Construct a 95% confidence interval for .
(B)Based on your answer to (A),are you convinced that the gaskets from shift 2 are,on average,wider than those from shift 1? Why or why not?

Question 61

(A)Construct a 90% confidence interval for the total value of all savings account balances within this bank.Assume that the population consists of all savings account balances in the frame.
(B)Interpret the 90% confidence interval constructed in (A).

Question 62

What is the probability of a t-value larger than 1.20?

Question 63

(A)Compute has a t-distribution with 15 degrees of freedom.
(B)Compute has a t-distribution with 150 degrees of freedom.
(C)How do you explain the difference between the results obtained in (A)and (B)?
(D)Compute where Z is a standard normal random variable.
(E)Compare the results of (D)to the results obtained in (A)and (B).How do you explain the difference in these probabilities?

Question 64

What is the probability of a t-value between -1.40 and +1.40?

Question 65

(A)You can be 95% confident that the mean salary for all production managers with at least 15 years of experience is between what two numbers (the t-multiple with 8 degrees of freedom is 2.306)? What assumption are you making about the distribution of salaries?
(B)What sample size would be needed to ensure that we could estimate the true mean salary of all production managers with more than 15 years of experience and have only 5 chances in 100 of being off by more than $4200?

Question 66

(A)Construct a 95% confidence interval for the mean playing time of all Willie Nelson recordings.
(B)Interpret the confidence interval you constructed in (A).

Question 67

(A)Construct a 90% confidence interval estimate of the mean family dental expenses for all employees of this corporation.
(B)What assumption about the population distribution must be made to answer (A)?
(C)Interpret the 90% confidence interval constructed in (A).
(D)Suppose you used a 95% confidence interval in (A).What would be your answer?
(E)Suppose the fourth value were 593 instead of 93.What would be your answer to (A)? What effect does this change have on the confidence interval?
(F)Construct a 90% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation.
(G)Interpret the 90% confidence interval constructed in (E).

Question 68

(A)Determine a 95% confidence interval for the proportion defective for the process today.
(B)Based on your answer to (A),is it still reasonable to think the overall proportion defective produced by today's process is actually the targeted 4%? Explain your reasoning.
(C)The confidence interval in (A)is based on the assumption of a large sample size.Is this sample size sufficiently large in this example? Explain how you arrived at your answer.
(D)How many units would have to be sampled to be 95% confident that you can estimate the fraction of defective parts within 2% (using the information from today's sample)?

Question 69

What would be the t-value where 0.05 of the values are in the upper tail?

Question 70

(A)Find a 95% confidence interval for the mean account balance on this store's credit card (the t-multiple with 39 degrees of freedom is 2.0227).
(B)What sample size would be needed to ensure that we could estimate the true mean account balance and have only 5 chances in 100 of being off by more than $100?

Question 71

(A)Construct a 99% confidence interval for the standard deviation of the number of hours this firm's employees spend on work-related activities in a typical week.
(B)Interpret the 99% confidence interval constructed in (A).
(C)Given the target range of 40 to 60 hours of work per week,should senior management be concerned about the number of hours their employees are currently devoting to work? Explain why or why not.

Question 72

(A)Use Excel to obtain a simple random sample of size 10 from this frame.
(B)Using the sample generated in (A),construct a 95% confidence interval for the mean average annual household income level of citizens in the selected U.S.cities.Assume that the population consists of all average annual household income levels in the given frame.
(C)Interpret the 95% confidence interval constructed in (B).
(D)Does the 95% confidence interval contain the actual population mean? If not,explain why not.What proportion of many similarly constructed confidence intervals should include the true population mean value?

Question 73

(A)Using a t - value of 2.0281,calculate a 95% confidence interval for the difference between the average Q-Mart charge and the average charge on another type of credit card.
(B)What are the degrees of freedom for the t - multiple in this calculation? Explain how you would calculate the degrees of freedom in this case.
(C)What is the assumption in this case that allows you to use the pooled standard deviation for this confidence interval?
(D)Would you conclude that there is a significant difference between the two types of customers in this case? Explain.

Question 74

(A)Construct a 95% confidence interval estimate of the population proportion of all customers who still own the cars they purchased six years ago
(B)How can the result in (A)be used by the automobile dealer to study satisfaction with cars purchased at the dealership?

Question 75

What is the probability of a t-value smaller than 1.00?

Question 76

(A)Construct a 95% confidence interval for the difference between the proportions of male and female customers who prefer Coke Classic over Pepsi Cola.
(B)Interpret the constructed confidence interval.

Question 77

What would be the t-values where 0.95 of the values would fall within this interval?

Question 78

What would be the t-values where 0.10 of the values are in both tails (sum of both tails)?

Question 79

(A)Use the sample data to generate a 95% confidence interval for the mean difference between the appraised values and selling prices of the houses sold in Grand Rapids.
(B)Interpret the constructed confidence interval fin (A)for the real estate agent.

Question 80

You are trying to estimate the average amount a family spends on food during a year.In the past the standard deviation of the amount a family has spent on food during a year has been approximately $800.If you want to be 95% sure that you estimated average family food expenditures within $50,how many families do you need to survey?