Deck 8: Confidence Interval Estimation

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

If the standard error of the sampling distribution of the sample proportion $\hat { pp }$
is 0.0324 for samples of size 200,then the population proportion must be 0.30.

Answer 3

False

Question 4

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 5

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

Question 6

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

Question 7

In developing a confidence interval for the population standard deviation $\sigma$
,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 8

The interval estimate 18.5 $\pm$
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 $\pm$
5.0.

Question 9

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, $x _ { 1 } - x _ { 2 }$
,equals 5.

Question 10

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 11

In developing confidence interval for the difference between two population means using two independent samples,we use the pooled estimate $s _ { p }$
in estimating the standard error of the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
if the populations are normal with equal variances.

Question 12

The approximate standard error of the point estimate of the population total is $N s / \sqrt { n }$ .

Question 13

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

Question 14

The 95% confidence interval for the population mean $\mu$
,given that the sample size n = 49 and the population standard deviation $$\sigma = 7 \text {, is } \bar { X } \pm 1.96$$

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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

Question 22

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 these choices

Question 23

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

A)
$\sigma / \sqrt { n }$
B)
$s / \sqrt { n }$
C)
$N \sigma / \sqrt { n }$
D)
$N s / \sqrt { n }$

Question 24

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 25

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 26

If you decrease the confidence level,the confidence interval .

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

Question 27

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 28

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

Question 29

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

Question 30

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

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

Question 31

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 32

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 33

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, $x _ { 1 } - x _ { 2 }$
,equals 1.4142.

Question 34

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 35

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 36

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

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 $\hat { p }$
is 0.60.

Question 38

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 39

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

Question 40

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 41

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 42

When we replace $\sigma$
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 43

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 44

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 45

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 46

A parameter such as $\sigma$
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 47

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 48

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 49

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 these choices

Question 50

Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means, $\mu _ { 1 } - \mu _ { 2 }$
)The sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
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 51

When you calculate the sample size for a proportion,you use an estimate for the population proportion;namely $P _ { \text {est } }$
)A conservative value for n can be obtained by using $P _ { \text {est } }$
=

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

Question 52

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

Question 53

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