Deck 8: Confidence Interval Estimation

Question 1

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.

Answer 1

True

Question 2

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.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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 8

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 9

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

Question 10

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

Question 11

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 12

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 13

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 14

A confidence interval is an interval that,with a stated level of confidence,captures a population parameter.

Question 15

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 16

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

Question 17

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 18

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

Question 19

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 20

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

Question 21

Samples of exam scores for employees before and after a training class are examples of paired data.

Question 22

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 23

The t-distribution for developing a confidence interval for a mean has degrees of freedom equal to

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

Question 24

When calculating a confidence interval for the difference between two population proportions,we multiply the standard error of the difference between sample proportions by t-multiple.

Question 25

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

Question 26

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 27

In developing a 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 28

The necessary sample size can only be determined for estimation problems regarding proportions because we do not know the value of the population standard deviation needed to calculate the necessary sample size for problems dealing with a population mean(s).

Question 29

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

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

Question 30

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

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

Question 31

Suppose that we want to estimate the difference in the proportion of all men and women that favor a homeless shelter opening up in their community.We should use a confidence interval for a difference between two population means to create our estimate.

Question 32

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

Question 33

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

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

Question 34

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 35

The value of the standard error of the difference between sample proportions depends on the sample proportion from each of the two populations as well as the sample size selected from each population.

Question 36

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.

Question 37

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 38

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 39

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 40

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 41

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 42

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

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

Question 43

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.

Question 44

You would like 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?

Question 45

You are attempting 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 46

If you increase the confidence level,the length of the confidence interval

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

Question 47

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 48

When the samples we want to compare pair in some natural way,such as a pretest/posttest for each person or husband/wife pairs,a more appropriate form of analysis is to not construct a confidence interval treating them as two separate variables,but instead to construct a confidence interval to estimate the mean

A)difference.
B)sum.
C)ratio.
D)total.

Question 49

If you are constructing a confidence interval for a single mean,the length of 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 50

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)an approximately standard normal random variable.
C)t-distributed with 45 degrees of freedom.
D)t-distributed with 43 degrees of freedom.

Question 51

What is an example of a problem in which the sample data is likely to be paired?

A)The difference between the means of appraised and sales house prices
B)The difference between the proportion of defective items from two suppliers
C)The difference in the mean life of two major brands of batteries
D)The difference in the mean salaries for graduates in two different academic fields at a university

Question 52

Confidence intervals are a function of the

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

Question 53

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

A) .
B) .
C) .
D) .

Question 54

In past years,approximately 25% of all U.S.families purchased potato chips at least once a month.We are interested in determining the fraction of all U.S.families that currently purchase potato chips at least once a month.How many families must we survey if we want to be 99% sure that our estimate of the fraction of U.S.families currently purchasing potato chips at least once a month is accurate within 2%?

Question 55

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 56

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

Question 57

The chi-square distribution for developing a confidence interval for a standard deviation has degrees of freedom equal to

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

Question 58

Generally speaking,the two types of statistical inference are

A)sample estimation and population estimation.
B)confidence interval estimation and hypothesis testing.
C)the interval estimation for a mean and the point estimation for a proportion.
D)independent sample estimation and dependent sample estimation.

Question 59

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)470.
D)0.94.

Question 60

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.