Question 1

As the alternative value of $\mu$increases, so does the power of the test.

Accepted Answer

True&#10;

Question 2

For a given level of significance, if the sample size increases, the probability of a Type II error will:&#10;A)remain the same.&#10;B)increase.&#10;C)decrease.&#10;D)be equal to 1.0 regardless of $\alpha$.

Accepted Answer

decrease.&#10;

Question 3

If a sample size is increased at a given $\alpha$ level, the probability of committing a Type II error is increased.

Accepted Answer

False&#10;

Question 4

For a given level of significance, if the sample size is increased, the power of the test will increase.

Accepted Answer

The answer of For a given level of significance, if...

Question 5

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ____________________.

Accepted Answer

The answer of For a given level of significance, if...

Question 6

For a given level of significance, if the sample size is increased, the power of the test will ____________________.

Accepted Answer

The answer of For a given level of significance, if...

Question 7

The operating characteristic curve plots the values of $\beta$ (the probability of committing a Type II error) versus the values of the population mean $\mu$.

Accepted Answer

The answer of The operating characteristic curve plots the values...

Question 8

One way of expressing how well a test performs is to report its power--the probability of detecting a false null hypothesis.

Accepted Answer

The answer of One way of expressing how well a...

Question 9

The power of the test refers to the probability of rejecting a false null hypothesis.

Accepted Answer

The answer of The power of the test refers to...

Question 10

For a given sample size n, if the level of significance $\alpha$is decreased, the power of the test will:&#10;A)increase.&#10;B)decrease.&#10;C)remain the same.&#10;D)Not enough information to tell.

Accepted Answer

The answer of For a given sample size n, if...

Question 11

If the probability of committing a Type I error for a given test is decreased, then for a fixed sample size n, the probability of committing a Type II error will:&#10;A)decrease.&#10;B)increase.&#10;C)stay the same.&#10;D)Not enough information to tell.

Accepted Answer

The answer of If the probability of committing a Type...

Question 12

Which of the following statements is false regarding the operating characteristic (OC) curve?&#10;A)The OC curve plots the values of $\beta$ versus the values of $\mu$.&#10;B)The OC curve plots the values of $\alpha$ versus the values of $\beta$.&#10;C)The OC curve can be useful in selecting a sample size n.&#10;D)None of these choices.

Accepted Answer

The answer of Which of the following statements is false...

Question 13

For a given level of significance $\alpha$, if the sample size n is increased, the probability of a Type II error $\beta$ will:&#10;A)decrease.&#10;B)increase.&#10;C)remain the same.&#10;D)Not enough information to tell.

Accepted Answer

The answer of For a given level of significance $\alpha$,...

Question 14

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Accepted Answer

The answer of For a given sample size, the probability...

Question 15

The power of a test is the probability that a true null hypothesis will be rejected.

Accepted Answer

The answer of The power of a test is the...

Question 16

If we want to compute the probability of a Type II error, which of the following statements is false?&#10;A)We need to know the significance level $\alpha$.&#10;B)We need to know the sample size n.&#10;C)We need to know the alternative value of the population mean $\mu$.&#10;D)All of these choices are true.

Accepted Answer

The answer of If we want to compute the probability...

Question 17

The power of a test is denoted by:&#10;A)$\alpha$&#10;B)$\beta$&#10;C)1 - $\alpha$&#10;D)1 - $\beta$

Accepted Answer

The answer of The power of a test is denoted...

Question 18

There is a direct relationship between the power of a test and the probability of a Type II error.

Accepted Answer

The answer of There is a direct relationship between the...

Question 19

The power of a test is measured by its capability of:&#10;A)rejecting a null hypothesis that is true.&#10;B)not rejecting a null hypothesis that is true.&#10;C)rejecting a null hypothesis that is false.&#10;D)not rejecting a null hypothesis that is false.

Accepted Answer

The answer of The power of a test is measured...

Question 20

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

Accepted Answer

The answer of For a given level of significance, if...

Question 21

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Calculate $\beta$, the probability of a Type II error when $\mu$ = 1000 and $\alpha$ = 0.10.

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 22

To calculate the probability of a(n) ____________________ error you need to specify a value of $\mu$other than the one given in the null hypothesis.

Accepted Answer

The answer of To calculate the probability of a(n) ____________________...

Question 23

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Recalculate $\beta$if n is increased from 25 to 40.

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 24

As the sample size increases, the operating characteristic curves drop down to zero at a(n) ____________________ rate.

Accepted Answer

The answer of As the sample size increases, the operating...

Question 25

To test the hypotheses: H₀: $\mu$ = 40 vs. H₁: $\mu$ $\neq$ 40, we draw a random sample of size 16 from a normal population whose standard deviation is 5. If we set $\alpha$= 0.01, find the probability of committing a Type II error when $\mu$ = 37.

Accepted Answer

The answer of To test the hypotheses: H₀: $\mu$ =...

Question 26

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Calculate the power of the test when $\mu$ = 1000 and $\alpha$ = 0.10.

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 27

Calculate the probability of a Type II error for the hypothesis test: H₀: $\mu$ = 50 vs. H₁: $\mu$ > 50, given that $\mu$ = 55, $\alpha$ = 0.05, $\sigma$ = 10, and n = 16.

Accepted Answer

The answer of Calculate the probability of a Type II...

Question 28

To increase the power of a test, ____________________ the sample size.

Accepted Answer

The answer of To increase the power of a test,...

Question 29

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Recalculate $\beta$ if $\alpha$ is lowered from 0.10 to 0.05.

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 30

By ____________________ the significance level, you increase the probability of a Type II error.

Accepted Answer

The answer of By ____________________ the significance level, you increase...

Question 31

The ____________________ of a test is a measure of its performance.

Accepted Answer

The answer of The ____________________ of a test is a...

Question 32

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Interpret the meaning of the power of the test.

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 33

A p-value is usually set at 0.05.

Accepted Answer

The answer of A p-value is usually set at 0.05....

Question 34

A(n) ____________________ characteristic curve plots the probability of a Type II error for various alternative values of ____________________.

Accepted Answer

The answer of A(n) ____________________ characteristic curve plots the probability...

Question 35

During the last energy crisis, a government official claimed that the average car owner refills the tank when there is more than 3 gallons left. To check the claim, 10 cars were surveyed as they entered a gas station. The amount of gas remaining before refill was measured and recorded as follows (in gallons): 3, 5, 3, 2, 3, 3, 2, 6, 4, and 1. Assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of 1 gallon. Compute the probability of a Type II error and the power of the test if the true average amount of gas remaining in tanks is 3.5 gallons.

Accepted Answer

The answer of During the last energy crisis, a government...

Question 36

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Review the results of the previous questions. What is the effect of decreasing the significance level on the value on $\beta$?

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 37

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

Accepted Answer

The answer of The p-value of a test is the...

Question 38

Probabilities for Type I and Type II errors are actually ____________________ probabilities.

Accepted Answer

The answer of Probabilities for Type I and Type II...

Question 39

The power of a test plus the probability of a Type II error equals ____________________.

Accepted Answer

The answer of The power of a test plus the...

Question 40

NARRBEGIN: Rechargeable Batteries Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Review the results of the previous questions. What is the effect of increasing the sample size on the value of $\beta$?

Accepted Answer

The answer of NARRBEGIN: Rechargeable Batteries&#10;Rechargeable Batteries&#10;A researcher wants to...

Question 41

A one-tail p-value is two times the size of a two-tail test.

Accepted Answer

The answer of A one-tail p-value is two times the...

Question 42

The larger the p-value, the more likely one is to reject the null hypothesis.

Accepted Answer

The answer of The larger the p-value, the more likely...

Question 43

In a one-tail test, the p-value is found to be equal to 0.054. If the test had been two-tail, then the p-value would have been 0.027.

Accepted Answer

The answer of In a one-tail test, the p-value is...

Question 44

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

Accepted Answer

The answer of If we reject the null hypothesis, we...

Question 45

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will decrease.

Accepted Answer

The answer of For a given level of significance, if...

Question 46

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

Accepted Answer

The answer of The critical values will bound the rejection...

Question 47

If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10 level.

Accepted Answer

The answer of If we reject a null hypothesis at...

Question 48

If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level.

Accepted Answer

The answer of If a null hypothesis is rejected at...

Question 49

The p-value of a test is the smallest $\alpha$ at which the null hypothesis can be rejected.

Accepted Answer

The answer of The p-value of a test is the...

Question 50

In order to determine the p-value, it is necessary to know the level of significance.

Accepted Answer

The answer of In order to determine the p-value, it...

Question 51

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 78.21 to 87.64. If the same sample had been used to test the null hypothesis that the mean of the population differs from 90, the null hypothesis could be rejected at a level of significance of 0.05.

Accepted Answer

The answer of A sample is used to obtain a...

Question 52

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

Accepted Answer

The answer of If we do not reject the null...

Question 53

A p-value is a probability, and must be between 0 and 1.

Accepted Answer

The answer of A p-value is a probability, and must...

Question 54

If your p-value is greater than 0.900 you should reject H₀ at the 0.10 level.

Accepted Answer

The answer of If your p-value is greater than 0.900...

Question 55

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 10.89 to 13.21. If the same sample had been used to test H₀:$\mu$= 12 vs. H₁: $\mu$$\neq$ 12, H₀ could not be rejected at the 0.05 level.

Accepted Answer

The answer of A sample is used to obtain a...

Question 56

The p-value is the probability that the null hypothesis is true.

Accepted Answer

The answer of The p-value is the probability that the...

Question 57

Using the confidence interval when conducting a two-tail test for the population mean $\mu$, we do not reject the null hypothesis if the hypothesized value for $\mu$ falls between the lower and upper confidence limits.

Accepted Answer

The answer of Using the confidence interval when conducting a...

Question 58

A one-tail test for the population mean $\mu$ produces a test-statistic z = -0.75. The p-value associated with the test is 0.7734.

Accepted Answer

The answer of A one-tail test for the population mean...

Question 59

For a given level of significance, if the sample size is increased, the probability of committing a Type I error will decrease.

Accepted Answer

The answer of For a given level of significance, if...

Question 60

A two-tail test for the population mean $\mu$ produces a test-statistic z = 1.89. The p-value associated with the test is 0.0588.

Accepted Answer

The answer of A two-tail test for the population mean...

Question 61

Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following $\alpha$-values do we also reject the null hypothesis?&#10;A)0.06&#10;B)0.04&#10;C)0.03&#10;D)0.02

Accepted Answer

The answer of Suppose that we reject a null hypothesis...

Question 62

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true:&#10;A)a Type I error is committed.&#10;B)a Type II error is committed.&#10;C)a correct decision is made.&#10;D)a one-tail test should be used instead of a two-tail test.

Accepted Answer

The answer of In a two-tail test for the population...

Question 63

In testing the hypotheses H₀: $\mu$ = 75 vs. H₁: $\mu$ < 75, if the value of the test statistic z equals -2.42, then the p-value is: A)0.5078 B)2.4200 C)0.9922 D)0.0078

Accepted Answer

The answer of In testing the hypotheses H₀: $\mu$ =...

Question 64

In testing the hypothesis H₀: $\mu$ = 100 vs. H₁: $\mu$ > 100, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true? A)The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. B)The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is 0.074. C)The probability that the population mean is larger than 100 is 0.074. D)None of these choices.

Accepted Answer

The answer of In testing the hypothesis H₀: $\mu$ =...