Question 1

A sample of 92 observations is taken from an infinite population. The sampling distribution of   is approximately

Accepted Answer

A) normal because   is always approximately normally distributed 
B) normal because the sample size is small in comparison to the population size 
C) normal because of the central limit theorem 
D) None of these alternatives is correct. 
A) normal because   is always approximately normally distributed 
B) normal because the sample size is small in comparison to the population size 
C) normal because of the central limit theorem 
D) None of these alternatives is correct. C

Question 2

Below you are given the values obtained from a random sample of 4 observations taken from an infinite population. 32 34 35 39
a.Find a point estimate for $\mu$. Is this an unbiased estimate of $\mu$? Explain.
b.Find a point estimate for $\sigma$2. Is this an unbiased estimate of $\sigma$2? Explain.
c.Find a point estimate for $\mu$.
d.What can be said about the sampling distribution of   ? Be sure to discuss the expected value, the standard deviation, and the shape of the sampling distribution of   .

Accepted Answer

a.35; Yes; E(x) = $\mu$ b.8.667; Yes; E(s²) = $\sigma$² c.2.944 d.E( ) = $\mu$, the standard deviation = $\sigma$²/n, and the sampling distribution of is normally distributed if the population is normally distributed.

Question 3

Which of the following is(are) point estimator(s)?

Accepted Answer

A) $\sigma$ 
B) $\mu$ 
C) s 
D) $\alpha$ 
A) $\sigma$ 
B) $\mu$ 
C) s 
D) $\alpha$ C

Question 4

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Accepted Answer

A) 0.0568 
B) 0.0778 
C) 0.4222 
D) 0.9222 
A) 0.0568 
B) 0.0778 
C) 0.4222 
D) 0.9222

Question 5

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

Accepted Answer

A) 0.2 and .04 
B) 0.2 and 0.2 
C) 20 and .04 
D) 20 and 0.2 
A) 0.2 and .04 
B) 0.2 and 0.2 
C) 20 and .04 
D) 20 and 0.2

Question 6

Michael is running for president. The proportion of voters who favor Michael is 0.8. A simple random sample of 100 voters is taken.
a.What are the expected value, standard deviation, and shape of the sampling distribution of   ? 
b.What is the probability that the number of voters in the sample who will not favor Michael will be between 26 and 30?
c.What is the probability that the number of voters in the sample who will not favor Michael will be more than 16?

Accepted Answer

a.0.8; 0.0

Question 7

A population characteristic, such as a population mean, is called

Accepted Answer

A) a statistic 
B) a parameter 
C) a sample 
D) the mean deviation 
A) a statistic 
B) a parameter 
C) a sample 
D) the mean deviation

Question 8

In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken.
a.What are the expected value, standard deviation, and shape of the sampling distribution of   ? 
b.What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.875?
c.What is the probability that the proportion of people who will order coffee with their meal is at least 0.945?

Accepted Answer

a.0.9; 0.0

Question 9

A department store has determined that 25% of all their sales are credit sales. A random sample of 75 sales is selected.
a.What is the probability that the sample proportion will be greater than 0.34?
b.What is the probability that the sample proportion will be between 0.196 and 0.354?
c.What is the probability that the sample proportion will be less than 0.25?
d.What is the probability that the sample proportion will be less than 0.10?

Accepted Answer

a.0.0359
b

Question 10

Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects.
a.Determine the standard error of the proportion.
b.What is the probability that the sample will contain more than 2.5% defective units?
c.What is the probability that the sample will contain more than 13% defective units?

Accepted Answer

a.0.03
b.0

Question 11

Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces.
a.Determine the mean and the variance of the population.
b.Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of   . 
c.Compute the standard error of the mean.

Accepted Answer

a.5 and 8

Question 12

An automotive repair shop has determined that the average service time on an automobile is 130 minutes with a standard deviation of 26 minutes. A random sample of 40 automotive services is selected.
a.Compute the standard error of the mean.
b.What is the probability that the sample of 40 automotive services will have a mean service time greater than 136 minutes?
c.Assume the population consists of 400 automotive services. Determine the standard error of the mean.

Accepted Answer

a.4.11
b.0

Question 13

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

Accepted Answer

A) 0.100 
B) 0.010 
C) 0.001 
D) 0.002 
A) 0.100 
B) 0.010 
C) 0.001 
D) 0.002

Question 14

Exhibit 7-1
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 7-1. In this problem the 0.22 is

Accepted Answer

A) a parameter 
B) a statistic 
C) the standard error of the mean 
D) the average content of colognes in the long run 
A) a parameter 
B) a statistic 
C) the standard error of the mean 
D) the average content of colognes in the long run

Question 15

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

Accepted Answer

A) population parameter 
B) biased estimate of the population mean 
C) sample parameter 
D) point estimate 
A) population parameter 
B) biased estimate of the population mean 
C) sample parameter 
D) point estimate

Question 16

The following information was collected from a simple random sample of a population. 16
19 18 17 20 18
The point estimate of the mean of the population is

Accepted Answer

A) 18.0 
B) 19.6 
C) 108 
D) sixteen, since 16 is the smallest value in the sample 
A) 18.0 
B) 19.6 
C) 108 
D) sixteen, since 16 is the smallest value in the sample

Question 17

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

Accepted Answer

A) 0.4332 
B) 0.9332 
C) 0.0668 
D) 0.5668 
A) 0.4332 
B) 0.9332 
C) 0.0668 
D) 0.5668

Question 18

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.
a.What are the expected value, standard deviation, and shape of the sampling distribution of   ? 
b.What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?
c.What is the probability that the average life in the sample will be greater than 3,219.24 hours?
d.What is the probability that the average life in the sample will be less than 3,180.96 hours?

Accepted Answer

a.3,000; 1

Question 19

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is

Accepted Answer

A) 1234±120 
B) 120 
C) 120*12=1440 
D) 10 
A) 1234±120 
B) 120 
C) 120*12=1440 
D) 10

Question 20

The standard deviation of all possible   values is called the

Accepted Answer

A) standard error of proportion 
B) standard error of the mean 
C) mean deviation 
D) central variation 
A) standard error of proportion 
B) standard error of the mean 
C) mean deviation 
D) central variation

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately

Which of the following is(are) point estimator(s)?

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

A population characteristic, such as a population mean, is called

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

Exhibit 7-1 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 7-1. In this problem the 0.22 is

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is

The standard deviation of all possible values is called the

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

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Nonparametric Methods

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Exam 7: Sampling and Sampling Distributions

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately

Which of the following is(are) point estimator(s)?

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

A population characteristic, such as a population mean, is called

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

Exhibit 7-1 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 7-1. In this problem the 0.22 is

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is

The standard deviation of all possible values is called the

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Index Numbers

Decision Analysis on Website

Sample Survey on Website

Filters