Question 1

Which of the following statements are not true?

Accepted Answer

A)  A statistical hypothesis is a claim or assertion either about the value of a single parameter, about the values of several parameters, or about the form of an entire probability distribution. 
B)  In any hypothesis-testing problem, there are two contradictory hypotheses under consideration. 
C)  A test of hypothesis is a method for using sample data to decide whether the null hypothesis should be rejected. 
D)  A type I error consists of not rejecting the null hypothesis $H _ { o } \text { when } H _ { o }$
Is false. 
E)  None of the above statements are true. 
A)  A statistical hypothesis is a claim or assertion either about the value of a single parameter, about the values of several parameters, or about the form of an entire probability distribution. 
B)  In any hypothesis-testing problem, there are two contradictory hypotheses under consideration. 
C)  A test of hypothesis is a method for using sample data to decide whether the null hypothesis should be rejected. 
D)  A type I error consists of not rejecting the null hypothesis $H _ { o } \text { when } H _ { o }$
Is false. 
E)  None of the above statements are true.

Question 2

Which of the following statements are needed in constructing the likelihood ratio test?

Accepted Answer

A)  Finding the largest value of the likelihood for any $\theta \text { in } \Omega _ { 0 }$
(by finding the maximum
Likelihood estimate within $\Omega _ { 0 }$
And substituting back into the likelihood function). 
B)  Find the largest value of the likelihood for any $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
C)  Forming the ratio $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$
= maximum likelihood for $\theta \text { in } \Omega _ { 0 } /$
Maximum likelihood for $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
D)  All of the above statements are needed. 
E)  Only statements A and B are needed. 
A)  Finding the largest value of the likelihood for any $\theta \text { in } \Omega _ { 0 }$
(by finding the maximum
Likelihood estimate within $\Omega _ { 0 }$
And substituting back into the likelihood function). 
B)  Find the largest value of the likelihood for any $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
C)  Forming the ratio $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$
= maximum likelihood for $\theta \text { in } \Omega _ { 0 } /$
Maximum likelihood for $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
D)  All of the above statements are needed. 
E)  Only statements A and B are needed.

Question 3

Suppose that when data from an experiment was analyzed, the P-value for testing $H _ {  o  } : \mu = 100 \text { versus } H _ { \pm } : \mu < 100$
 was calculated as .047. At the .01 level, $H _ { o }$ would __________.

Accepted Answer

The answer of Suppose that when data from an experiment...

Question 4

In hypothesis-testing analysis, a type II error occurs only if

Accepted Answer

A)  the null hypothesis is rejected when it is true. 
B)  the null hypothesis is rejected when it is false. 
C)  the null hypothesis is not rejected when it is false. 
D)  the null hypothesis is not rejected when it is true. 
A)  the null hypothesis is rejected when it is true. 
B)  the null hypothesis is rejected when it is false. 
C)  the null hypothesis is not rejected when it is false. 
D)  the null hypothesis is not rejected when it is true.

Question 5

As the level of significance $\alpha$ decreases, the critical value __________.

Accepted Answer

The answer of As the level of significance $\alpha$ decreases,...

Question 6

Suppose a test procedure about the population mean $\mu$ is performed, when the population is normal and the sample size n is small, then if the alternative hypothesis is $H _ { \pm } : \mu > \mu _ { o }$ the rejection region for a level $\alpha$ test is __________.

Accepted Answer

The answer of Suppose a test procedure about the population...

Question 7

The rejection region is called __________ if it consists only of large values of the test statistic.

Accepted Answer

The answer of The rejection region is called __________ if...

Question 8

Which of the following statements are not true?

Accepted Answer

A)  A test statistic is a function of the sample data on which the decision to reject or not reject the null hypothesis is to be based. 
B)  A rejection region consists of the set of all test statistic values for which the null hypothesis will be rejected. 
C)  A rejection region consists of the set of all test statistic values for which the alternative hypothesis will be rejected. 
D)  A good hypothesis-testing procedure is one for which the probability of making either type I or type II error is small. 
E)  None of the above statements are true. 
A)  A test statistic is a function of the sample data on which the decision to reject or not reject the null hypothesis is to be based. 
B)  A rejection region consists of the set of all test statistic values for which the null hypothesis will be rejected. 
C)  A rejection region consists of the set of all test statistic values for which the alternative hypothesis will be rejected. 
D)  A good hypothesis-testing procedure is one for which the probability of making either type I or type II error is small. 
E)  None of the above statements are true.

Question 9

Which of the following statements are not true?

Accepted Answer

A)  A rejection region is called upper-tailed if it consists only of large values of the test statistic. 
B)  A rejection region is called upper-tailed if it consists only of small values of the test statistic. 
C)  A rejection region is called lower-tailed if it consists only of small values of the test statistic. 
D)  All of the above statements are true. 
E)  None of the above statements are true. 
A)  A rejection region is called upper-tailed if it consists only of large values of the test statistic. 
B)  A rejection region is called upper-tailed if it consists only of small values of the test statistic. 
C)  A rejection region is called lower-tailed if it consists only of small values of the test statistic. 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 10

The probabilities of type I and type II errors are traditionally denoted by the Greek letters __________ and __________, respectively.

Accepted Answer

The answer of The probabilities of type I and type...

Question 11

The desired percentage Si $O _ { 2 }$ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility using a significance level of .01, 16 independently obtained samples are analyzed. Suppose that the percentage of Si $O _ { 2 }$ in a sample is normally distributed with $\sigma = 3$ and that $\bar { x } = 5.25 .$ 
a. Does this indicate conclusively that the true average percentage differs from 5.5?
b. If the true average percentage is $\mu = 5.6$ 
and a level $\alpha = .01$ 
based on n = 16 is used, what is the probability of detecting this departure from $H _ { 0 } ?$ 
c. What value of n is required to satisfy $\alpha = .01$ 
and $\beta ( 5.6 ) = .01 ?$

Accepted Answer

a. @#IMG-DLM& for a level .01

Question 12

Which of the following statements are not correct?

Accepted Answer

A)  It is possible that the null hypothesis may be rejected when it is true. 
B)  It is impossible that the null hypothesis may be rejected when it is true. 
C)  It is possible that the null hypothesis may not be rejected when it is false. 
D)  All of the above statements are correct. 
E)  None of the above statements are correct. 
A)  It is possible that the null hypothesis may be rejected when it is true. 
B)  It is impossible that the null hypothesis may be rejected when it is true. 
C)  It is possible that the null hypothesis may not be rejected when it is false. 
D)  All of the above statements are correct. 
E)  None of the above statements are correct.

Which of the following statements are not true?

Which of the following statements are needed in constructing the likelihood ratio test?

Suppose that when data from an experiment was analyzed, the P-value for testing $H _ { o } : \mu = 100 \text { versus } H _ { \pm } : \mu < 100$ was calculated as .047. At the .01 level, $H _ { o }$ would __________.

In hypothesis-testing analysis, a type II error occurs only if

As the level of significance $\alpha$ decreases, the critical value __________.

Suppose a test procedure about the population mean $\mu$ is performed, when the population is normal and the sample size n is small, then if the alternative hypothesis is $H _ { \pm } : \mu > \mu _ { o }$ the rejection region for a level $\alpha$ test is __________.

The rejection region is called __________ if it consists only of large values of the test statistic.

Which of the following statements are not true?

Which of the following statements are not true?

The probabilities of type I and type II errors are traditionally denoted by the Greek letters and , respectively.

Which of the following statements are not correct?

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Inferences Based on Two Samples

The Analysis of Variance

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Quality Control Methods

Filters

Exam 8: Tests of Hypotheses Based on a Single Sample

Which of the following statements are not true?

Which of the following statements are needed in constructing the likelihood ratio test?

Suppose that when data from an experiment was analyzed, the P-value for testing Ho:μ=100 versus H±:μ<100H _ { o } : \mu = 100 \text { versus } H _ { \pm } : \mu < 100Ho​:μ=100 versus H±​:μ<100 was calculated as .047. At the .01 level, HoH _ { o }Ho​ would __________.

In hypothesis-testing analysis, a type II error occurs only if

As the level of significance α\alphaα decreases, the critical value __________.

Suppose a test procedure about the population mean μ\muμ is performed, when the population is normal and the sample size n is small, then if the alternative hypothesis is H±:μ>μoH _ { \pm } : \mu > \mu _ { o }H±​:μ>μo​ the rejection region for a level α\alphaα test is __________.

The rejection region is called __________ if it consists only of large values of the test statistic.

Which of the following statements are not true?

Which of the following statements are not true?

The probabilities of type I and type II errors are traditionally denoted by the Greek letters __________ and __________, respectively.

Which of the following statements are not correct?

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Inferences Based on Two Samples

The Analysis of Variance

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Quality Control Methods

Filters

Suppose that when data from an experiment was analyzed, the P-value for testing $H _ { o } : \mu = 100 \text { versus } H _ { \pm } : \mu < 100$ was calculated as .047. At the .01 level, $H _ { o }$ would __________.

As the level of significance $\alpha$ decreases, the critical value __________.

Suppose a test procedure about the population mean $\mu$ is performed, when the population is normal and the sample size n is small, then if the alternative hypothesis is $H _ { \pm } : \mu > \mu _ { o }$ the rejection region for a level $\alpha$ test is __________.

The probabilities of type I and type II errors are traditionally denoted by the Greek letters and , respectively.