Exam 2 (Chapters 7&8)
If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.
.05 * .9* .95 .1
Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is _____.
.22 *4* 121 .02
Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for . In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size for a given level of confidence and a given margin of error is
.10 1 *.50* .90
A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.
.4332 .9332 *.0668* .5668
Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately _____.
*8.74 to 9.26 hours* 7.80 to 10.20 hours 7.04 to 110.96 hours 7.36 to 10.64 hours
An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random sample of 200 current owners is selected. The population standard deviation is known. Which Excel function would NOT be appropriate to use to construct a confidence interval estimate?
*COUNTIF* STDEV AVERAGE NORM.S.INV
A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?
*If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.* 95% of the sample of employees has a systolic blood pressure between 123 and 139. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139. 95% of the population of employees has a systolic blood pressure between 123 and 139.
From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for μ. Which of the following statements is true?
*The t distribution with 49 degrees of freedom must be used.* The t distribution with 50 degrees of freedom must be used. The standard normal distribution can be used. The sample size must be increased in order to develop an interval estimate.
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____.
*degrees of freedom* population standard deviation confidence level desired margin of error
In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom.
*n − 1* sq rt. n italicized n sq rt. n - 1
For which of the following values of p is the value of P(1 − p) maximized?
*p = .50* p = .99 p = .90 p = 1.0
A sample statistic, such as , that estimates the value of the corresponding population parameter is known as a _____.
*point estimator* parameter population parameter parameter and a population parameter
From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, the proper distribution to use is the _____.
*t distribution with 24 degrees of freedom* t distribution with 26 degrees of freedom standard normal distribution z distribution
In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed?
*the mean of the population* a preliminary estimate of the true population proportion p the confidence level required the maximum margin of error that can be tolerated
The t distribution should be used whenever _____. Correct!
*the sample standard deviation is used to estimate the population standard deviation* the population is not normally distributed the sample size is less than 30 None of the answers is correct.
The t distribution should be used whenever _____.
*the sample standard deviation is used to estimate the population standard deviation* the sample size is less than 30 the population is not normally distributed None of the answers is correct.
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the _____.
*width of the confidence interval to increase* width of the confidence interval to decrease sample size to increase width of the confidence interval to remain the same
The sample mean is the point estimator of _____.
*μ* σ _ x _ p
Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. Refer to Exhibit 8-1. The standard error of the mean is _____.
.014 7.5 *.133* .160
The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____.
.99 .51 *.50* .01
A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is _____.
0 *.0495* .4505 None of the answers is correct.
It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population. There is a .95 probability that the sample mean will provide a margin of error of _____.
1,936 or less 31.36 or less *7.84 or less* 344.96 or less
Exhibit 8-2 The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time for all customers is _____.
1.36 to 4.64 *2.804 to 3.196* 1.04 to 4.96 3 to 5
The t value with a 95% confidence and 24 degrees of freedom is _____.
1.711 2.492 2.069 *2.064*
Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. Refer to Exhibit 8-1. With a .95 probability, the margin of error is approximately_____.
1.96 .21 *.26* 1.64
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____.
1.96 1.645 .485 *.95*
The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is _____.
15 *10* 20 125
It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is
189 74 25 *75*
The z value for a 97.8% confidence interval estimation is _____.
2.00 * 2.29* 1.96 2.02
Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. If we are interested in determining an interval estimate for μ at 86.9% confidence, the z value to use is _____.
2.00 1.96 1.31 *1.51*
A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is _____.
21.2 to 22.8 *19.2 to 20.8* 19.216 to 20.784 15.2 to 24.8
From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is _____.
3 2 greater than 2 *less than 2*
Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Refer to Exhibit 7-4. The standard error of the mean equals _____.
3636 .0331 * .0200* 4.000
A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21 A point estimate of the population mean is _____.
5 *18* 19 20
Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. The 86.9% confidence interval for μ is _____.
50 to 70 *57.735 to 62.265* 59.131 to 60.869 46.500 to 73.500
A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____.
500 and .047 500 and .050 * .5 and .047* .5 and .050
Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are _____.
6 and 15 20 and 15 20 and 0.417 *20 and 2.5*
A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is _____.
70.02 to 81.98 *69.29 to 82.71* 70.06 to 81.94 69.82 to 82.18
A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____.
8.462 to 11.538 *8.384 to 11.616* 6.000 to 14.000 9.846 to 10.154
Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are _____.
8.7 and 1.94 36 and 1.94 *36 and 1.86* 36 and 8
A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____.
8633 .6900 *.0819* .0345
Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. The value to use for the standard error of the mean is _____.
9 *2.26* 13.5 1.5
A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid
95% of the population of employees has a systolic blood pressure between 123 and 139. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139. * If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.* 95% of the sample of employees has a systolic blood pressure between 123 and 139.
A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?
95% of the sample of employees has a systolic blood pressure between 123 and 139. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139. 95% of the population of employees has a systolic blood pressure between 123 and 139. *If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.*
A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random sample of 50 items is selected. Which Excel function would NOT be appropriate to construct a confidence interval estimate?
COUNTIF All of these answers are correct.r *STDEV* NORM.S.INV
A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50 times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2 minutes. Which Excel function would be used to construct a confidence interval estimate?
INT NORM.INV T.INV *CONFIDENCE.NORM*
A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is selected. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate?
NORM.INV INT *NORM.S.INV* T.INV
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____.
None of the answers is correct. stays the same *becomes smaller* becomes larger
If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____.
_ x plus or minus 4.6
In developing an interval estimate of the population mean, if the population standard deviation is unknown _____.
a sample proportion can be used None of the answers is correct. *the sample standard deviation and t distribution can be used* it is impossible to develop an interval estimate
The purpose of statistical inference is to provide information about the _____.
ample based upon information contained in the population *population based upon information contained in the sample* population based upon information contained in the population mean of the sample based upon the mean of the population
For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.
approximately normal for all sample sizes exactly normal for large sample sizes exactly normal for all sample sizes *approximately normal for large sample size*
The degrees of freedom associated with a t distribution are a function of the _____.
area in the upper tail *sample size* confidence coefficient sample standard deviation
A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____.
becomes wider does not change becomes .1 *becomes narrower*
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____.
binomial distribution Poisson distribution hypergeometric distribution *normal probability distribution*
When the level of confidence increases, the confidence interval _____.
cannot be determined from the information given stays the same *becomes wider* becomes narrower
The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.
confidence level error factor level of significance *confidence coefficient*
An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the _____.
confidence level population estimate *interval estimate* parameter value
Excel's RAND function _____.
determines sample size selects a simple random sample randomizes a population *generates random numbers*
Using α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion _____.
does not change *becomes wider* becomes narrower Not enough information is provided to answer this question.
As the degrees of freedom increase, the t distribution approaches the _____ distribution.
exponential p uniform *normal*
As the sample size increases, the variability among the sample means _____.
increases *decreases* remains the same depends upon the specific population being sampled
The confidence associated with an interval estimate is called the ___
level of significance *confidence level* degree of association precision
The confidence associated with an interval estimate is called the _____.
level of significance precision degree of association *confidence level*
Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for μ would _____.
not change become zero become narrower *become wider*
A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a _____.
population parameter point estimator sample parameter * point estimate*
The general form of an interval estimate of a population mean or population proportion is the _____ plus or minus the _____.
planning value, confidence coefficient population mean, standard error level of significance, degrees of freedom *point estimate, margin of error*
The ability of an interval estimate to contain the value of the population parameter is described by the _____.
precise value of the population mean μ *confidence level* degrees of freedom None of the answers is correct.
Which of the following is an example of a nonprobability sampling technique?
simple random sampling stratified random sampling cluster sampling *judgment sampling*
The standard deviation of all possible values is called the _____.
standard error of proportion *standard error of the mean* mean deviation central variation
The standard deviation of is referred to as the _____.
standard proportion sample proportion average proportion *standard error of the proportion*
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____
stays the same becomes larger None of the answers is correct. *becomes smaller*
Which of the following sampling methods does NOT lead to probability samples?
stratified sampling cluster sampling systematic sampling *convenience sampling*
A subset of a population selected to represent the population is a _____.
subset *sample* small population None of the answers is correct.
An interval estimate is used to estimate _____.
the shape of the population's distribution *a population parameter* a sample statistic the sampling distribution
The margin of error in an interval estimate of the population mean is a function of all of the following EXCEPT _____.
variability of the population sample size level of significance *sample mean*
Exhibit 8-2 The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. If the confidence coefficient is reduced to .80, the standard error of the mean _____.
will increase *remains unchanged* will decrease becomes negative
Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean?
z distribution binomial distribution *t distribution* standard distribution
Which of the following is a point estimator?
σ 4 *s* __ x