Question 1

The value $\alpha$ that represents the probability of type I error is often referred to as the __________ of the test.

Accepted Answer

The answer of The value $\alpha$ that represents the probability...

Question 2

Which of the following statements are true?

Accepted Answer

A)  The null hypothesis, denoted by $H _ { o }$
, is the claim that is initially assumed to be true (the "prior belief" claim). 
B)  The alternative hypothesis, denoted by $H _ { \pm }$
, is the assertion that is contradictory to the null hypothesis $H _ { o }$
) 
C)  The null hypothesis $H _ { o }$
Will be rejected in favor of the alternative hypothesis only if sample evidence suggests that $H _ { o }$
Is false. 
D)  If sample evidence does not strongly contradict the null hypothesis $H _ { o }$
, we will continue to believe in the truth of $H _ { o }$
) 
E)  All of the above statements are true.

Question 3

A __________ error is usually more serious than a __________ error.

Accepted Answer

The answer of A __________ error is usually more serious...

Question 4

If $\theta$ denotes the parameter of interest, and the simplified null hypothesis has the form $H _ { o } : \theta = \theta _ { 0 } , \text { where } \theta _ { o }$ is a specified number called the "null value" of the parameter, then the alternative hypothesis will be

Accepted Answer

A)  $H _ { \pm } : \theta > \theta _ { o }$
(so the implicit null hypothesis is $\left. \theta \leq \theta _ { o } \right)$ 
B)  $H _ { \pm } : \theta < \theta _ { o }$
(so the implicit null hypothesis is $\left. \theta \geq \theta _ { o } \right)$ 
C)  $H _ { \pm } : \theta \neq \theta _ { o }$ 
D)  The alternative hypothesis will look like any of the above three assertions. 
E)  The alternative hypothesis must be the assertion specified in (
C) .

Question 5

Which of the following statements are not true?

Accepted Answer

A)  The test statistic $Z = \left( \bar { X } - \mu _ { 0 } \right)/ ( \sigma / \sqrt { n } )$
Has a standard normal distribution when $H _ { o } : \mu = \mu _ { 0 }$
Is true. 
B)  The reliability of hypothesis testing procedure in reaching a correct decision can be assessed by studying type I error probability. 
C)  The process of reaching a decision by using the methodology of classical hypothesis testing involves selecting a level of significance $\alpha$
And then rejecting or not rejecting the null hypothesis $H _ { o }$
At that level $\alpha .$ 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 6

In our treatment of hypothesis testing, the __________ hypothesis will always be stated as an equality claim.

Accepted Answer

The answer of In our treatment of hypothesis testing, the...

Question 7

Let p denote the proportion of individuals in a population who possess a specified property, and X denote the number of individuals in the sample who possess the same property. Provided that the sample size n is small relative to the population size, then X has approximately a __________ distribution.

Accepted Answer

The answer of Let p denote the proportion of individuals...

Question 8

The times of first sprinkler activation for a series of tests with fire prevention sprinkler systems using an aqueous film-forming were (in sec). $\begin{array} { l l l l l l l l l l l l l } 
28 & 42 & 23 & 28 & 24 & 36 & 31 & 34 & 25 & 28 & 29 & 23 & 25
\end{array}$ The system has been designed so that "true" average activation time is at most 25 sec under such conditions. Does the data strongly contradict the validity of this design specification? Test the relevant hypotheses at significance level .05 using the P-value approach.

Accepted Answer

The answer of The times of first sprinkler activation for...

Question 9

Suppose that a test procedure about the population proportion p is performed, and that the sample proportion $\hat { p }$ is approximately normally distributed. If the alternative hypothesis is $H a : p > p _ { o }$ , then the rejection region for a level $\alpha$ test is __________.

Accepted Answer

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

Question 10

If the calculated test statistic for an upper-tailed z test is 2.15, then the P-value is __________.

Accepted Answer

The answer of If the calculated test statistic for an...

Question 11

Suppose that a two-tailed test procedure about the population mean $\mu$ is performed when the population is normal, but the sample size n is small. The null hypothesis will be rejected at significance level $\alpha$ if the value of the standardized test statistic t is such that

Accepted Answer

A)  $t \geq t _ { \alpha , n - 1 }$ 
B)  $t \leq - t _ { \alpha _ { i } , n- 1 }$ 
C)  either $t \geq t _ { \alpha / 2 , n - 1 } \text { or } t \leq - t _ { \alpha / 2 , n - 1 }$ 
D)  $- t _ { \alpha/ 2 , n - 1 } \leq t \leq t _ { \alpha/2, n - 1 }$ 
E)  None of the above inequalities are correct.

Question 12

Which of the following statements are not true?

Accepted Answer

A)  If the alternative hypothesis has the form $H _ { ± } : p > p _ { o }$
, then a $\hat { p } \text { value less than } p _ { o }$
Certainly does not provide support for $H _ { \pm}$
) 
B)  If the alternative hypothesis has the form $H _ { ± } : p > p _ { o }$
, then a $\hat { p } \text { value that ex ceeds } p _ { o }$
By only a small amount (corresponding to z value which is positive but small) does not suggest that $H _ { o }$
Should be rejected in favor of $H _ { \pm }$
) 
C)  If the null hypothesis is $H _ { o } : p = .50 , \hat { p } = .51$

And n = 100, then the test statistic value is z = 4 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 13

The null hypothesis will be rejected if and only if the observed or computed __________ value falls in the __________.

Accepted Answer

The answer of The null hypothesis will be rejected if...

Question 14

Let $\mu$ denote the mean reaction time to a certain stimulus. For a large-sample z test of $H _ { 0 } : \mu = 8$ versus $H _ { \pm } : \mu > 8$ find the P-value associated with each of the given values of the z test statistics. 
a. 1.52
b. .95
c. 1.96
d. 2.33
e. .79

Accepted Answer

The answer of Let $\mu$ denote the mean reaction time...

Question 15

The __________ hypothesis should be identified with the hypothesis of no change, no difference, no improvement, and son on.

Accepted Answer

The answer of The __________ hypothesis should be identified with...

Question 16

The likelihood ratio test procedure consists of rejecting the null hypothesis $H _ { o }$ when the likelihood ratio statistic value $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$ is __________.

Accepted Answer

The answer of The likelihood ratio test procedure consists of...

Question 17

Which of the following statements are not true?

Accepted Answer

A)  A P-value conveys much information about the strength of evidence against the null hypothesis $H _ { o }$
And allows an individual decision maker to draw a conclusion at any specified significance level $\alpha .$  
B)  The P-value (or observed significance level) is the largest level of significance at which the null hypothesis $H _ { o }$
Would be rejected when a specified test procedure is used on a given data set. 
C)  If P-value $\leq \alpha , \text { wereject } H _ { o } \text { at level } \alpha \text {. }$ 
D)  If P-value $> \alpha \text {, we do not reject } H _ { o } \text { at level } \alpha \text {. }$ 
E)  All of the above statements are true.

Question 18

Which of the following statements are true?

Accepted Answer

A)  Knowledge of the test statistic's distribution when the null hypothesis is true allows us to construct a rejection region for which the type I error probability is controlled at the desired level. 
B)  The rejection region for the t test differs from that for the z test only in that a t critical value replaces the z critical value. 
C)  If $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$
(n is small) is a random sample from a normal distribution, the standardized variable $T = ( \bar { X } - \mu ) / ( S / \sqrt { n } )$
Has a t distribution with n-1 degrees of freedom. 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 19

It is customary to call the data significant when the null hypothesis is __________, and not significant otherwise.

Accepted Answer

The answer of It is customary to call the data...

Question 20

Consider the large-sample level .01 test for testing $H _ { 0 } : p = .2$ versus $H _ { a } : p > .2$ 
a. For the alternative value p = .21, compute $\beta ( .21 )$ 
sample sizes n = 100, 2500, 10,000, 40,000, and 90,000. 
b. For $\hat { p } = x / n = .21$ 
, compute the p-value when n = 100, 2500, 10,000, and 40,000.

Accepted Answer

The answer of Consider the large-sample level .01 test for...

Exam 8: Tests of Hypotheses Based on a Single Sample

The value $\alpha$ that represents the probability of type I error is often referred to as the __________ of the test.

Which of the following statements are true?

A error is usually more serious than a error.

If $\theta$ denotes the parameter of interest, and the simplified null hypothesis has the form $H _ { o } : \theta = \theta _ { 0 } , \text { where } \theta _ { o }$ is a specified number called the "null value" of the parameter, then the alternative hypothesis will be

Which of the following statements are not true?

In our treatment of hypothesis testing, the __________ hypothesis will always be stated as an equality claim.

Suppose that a test procedure about the population proportion p is performed, and that the sample proportion $\hat { p }$ is approximately normally distributed. If the alternative hypothesis is $H a : p > p _ { o }$ , then the rejection region for a level $\alpha$ test is __________.

If the calculated test statistic for an upper-tailed z test is 2.15, then the P-value is __________.

Suppose that a two-tailed test procedure about the population mean $\mu$ is performed when the population is normal, but the sample size n is small. The null hypothesis will be rejected at significance level $\alpha$ if the value of the standardized test statistic t is such that

Which of the following statements are not true?

The null hypothesis will be rejected if and only if the observed or computed value falls in the .

Let $\mu$ denote the mean reaction time to a certain stimulus. For a large-sample z test of $H _ { 0 } : \mu = 8$ versus $H _ { \pm } : \mu > 8$ find the P-value associated with each of the given values of the z test statistics. a. 1.52 b. .95 c. 1.96 d. 2.33 e. .79

The __________ hypothesis should be identified with the hypothesis of no change, no difference, no improvement, and son on.

The likelihood ratio test procedure consists of rejecting the null hypothesis $H _ { o }$ when the likelihood ratio statistic value $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$ is __________.

Which of the following statements are not true?

Which of the following statements are true?

It is customary to call the data significant when the null hypothesis is __________, and not significant otherwise.

Exam 8: Tests of Hypotheses Based on a Single Sample

The value α\alphaα that represents the probability of type I error is often referred to as the __________ of the test.

Which of the following statements are true?

A __________ error is usually more serious than a __________ error.

Which of the following statements are not true?

In our treatment of hypothesis testing, the __________ hypothesis will always be stated as an equality claim.

If the calculated test statistic for an upper-tailed z test is 2.15, then the P-value is __________.

Suppose that a two-tailed test procedure about the population mean μ\muμ is performed when the population is normal, but the sample size n is small. The null hypothesis will be rejected at significance level α\alphaα if the value of the standardized test statistic t is such that

Which of the following statements are not true?

The null hypothesis will be rejected if and only if the observed or computed __________ value falls in the __________.

The __________ hypothesis should be identified with the hypothesis of no change, no difference, no improvement, and son on.

The likelihood ratio test procedure consists of rejecting the null hypothesis HoH _ { o }Ho​ when the likelihood ratio statistic value λ(x1,…,…,xn)\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)λ(x1​,…,…,xn​) is __________.

Which of the following statements are not true?

Which of the following statements are true?

It is customary to call the data significant when the null hypothesis is __________, and not significant otherwise.

The value $\alpha$ that represents the probability of type I error is often referred to as the __________ of the test.

A error is usually more serious than a error.

Suppose that a two-tailed test procedure about the population mean $\mu$ is performed when the population is normal, but the sample size n is small. The null hypothesis will be rejected at significance level $\alpha$ if the value of the standardized test statistic t is such that

The null hypothesis will be rejected if and only if the observed or computed value falls in the .

The likelihood ratio test procedure consists of rejecting the null hypothesis $H _ { o }$ when the likelihood ratio statistic value $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$ is __________.