Question 1

The rejection region for testing H₀: μ = 100 vs.H₁: μ ≠ 100,at the 0.05 level of significance is: A)| z | < 0.95 B)| z | > 1.96 C)z > 1.65 D)z < 2.33

Accepted Answer

Since the alternative hypothesis is two-sided (μ ≠ 100), we need to use a two-tailed test. At the 0.05 level of significance, the critical values for a two-tailed test are ±1.96. Therefore, the rejection region for the test is |z| > 1.96.

Question 2

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:
A)either a one-tail or two-tail test could be used with equivalent results.
B)a one-tail test should be utilized.
C)a two-tail test should be utilized.
D)None of these choices.

Accepted Answer

A one-tail test should be utilized because the marketer is interested in determining if the average family income exceeds a specific value, not if it is different from that value.

Question 3

We have created a 95% confidence interval for μ with the results (10,25).What conclusion will we make if we test H₀: μ = 26 vs.H₁: μ ≠ 26 at α = 0.025? A)Reject H₀ in favor of H₁ B)Accept H₀ in favor of H₁ C)Fail to reject H₀ in favor of H₁ D)We cannot tell from the information given.

Accepted Answer

The answer of We have created a 95% confidence interval...

Question 4

The ____________________ is a range of values such that if the test statistic falls into that range we reject the null hypothesis in favor of the alternative
hypothesis.

Accepted Answer

The answer of The ____________________ is a range of values...

Question 5

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the ____________________ method.The other approach is the p-value method.

Accepted Answer

The answer of There are two approaches to making a...

Question 6

The rejection region for testing H₀: μ = 80 vs.H₁: μ < 80,at the 0.10 level of significance is: A)z > 1.96 B)z < 0.90 C)z > 1.28 D)z < −1.28

Accepted Answer

Since the alternative hypothesis is one-tailed and specifies that the mean is less than 80, we need to find the z-score that corresponds to the 10th percentile of the standard normal distribution. This is approximately -1.28, so the rejection region is z < -1.28. Therefore, the answer is D.

Question 7

When a null hypothesis is rejected,the test is said to be statistically ____________________ at level α.

Accepted Answer

The answer of When a null hypothesis is rejected,the test...

Question 8

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

Accepted Answer

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

Question 9

The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club.She would now like to determine whether or not the mean age of her customers is over 35.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years.What is the p-value associated with the test statistic?
A)0.9582
B)1.7300
C)0.0418
D)0.0836

Accepted Answer

We need to conduct a one-sample t-test, where the null and alternative hypotheses are:

$H_0: \mu \leq 35$ (the mean age is not over 35)
$H_1: \mu > 35$ (the mean age is over 35)

The test statistic can be calculated as:

$t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} = \frac{35.5 - 35}{\frac{5}{\sqrt{300}}} \approx 2.23$

The degrees of freedom for the t-distribution is $n-1 = 299$, and using a t-table or calculator, we can find the p-value associated with this test statistic to be approximately 0.0418.

Therefore, the best choice is C, with the p-value of 0.0418.

Question 10

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the rejection region method.The other approach is the ____________________ method.

Accepted Answer

The answer of There are two approaches to making a...

Question 11

If the conclusion of a hypothesis test is that a statistically significant result was found,then the null hypothesis ____________________ (was/was not)rejected.

Accepted Answer

The answer of If the conclusion of a hypothesis test...

Question 12

We have created a 90% confidence interval for μ with the result (25,32).What conclusion will we make if we test H₀: μ = 28 vs.H₁: μ ≠ 28 at α = 0.10? A)Reject H₀ in favor of H₁. B)Accept H₀ in favor of H₁. C)Fail to reject H₀ in favor of H₁. D)We cannot tell from the information given.

Accepted Answer

Since the 90% confidence interval does not contain the hypothesized value of 28, we can conclude that it is plausible that the true value of μ is not equal to 28. However, this conclusion does not necessarily mean that we can reject H₀ in favor of H₁ at α = 0.10. To make such a conclusion, we would need to perform a formal hypothesis test using the given significance level. Since the calculated p-value is not given, we cannot determine if the null hypothesis should be rejected or not. Therefore, the best choice is option C, which states that we fail to reject H₀ in favor of H₁.

Question 13

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if:
A)a two-tail test for μ is used.
B)a one-tail test for μ is used.
C)a two-tail test for  is used.
D)a one-tail test for

Is used.

Accepted Answer

A two-tail test for μ is used when the null hypothesis is that the true population mean is equal to a hypothesized value, and the alternative hypothesis is that the true population mean is not equal to the hypothesized value. This is equivalent to constructing a confidence interval estimate for the population mean and checking whether the hypothesized value falls within the interval. Therefore, the results of a confidence interval estimate can be directly compared to the results of a two-tail test for μ.

Question 14

If the p value is less than α in a two-tail test:
A)the null hypothesis should not be rejected.
B)the null hypothesis should be rejected.
C)a one-tail test should be used.
D)No conclusion should be reached.

Accepted Answer

If the p value is less than α in a two-tail test, it means that the observed result is statistically significant and unlikely to have occurred by chance. Therefore, the null hypothesis should be rejected in favor of the alternative hypothesis.

Question 15

The owner of a local Karaoke Bar has recently surveyed a random sample of n = 300 customers of the bar.She would now like to determine whether or not the mean age of her customers is over 35.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.If she wants to be 99% confident in her decision,what rejection region she use if the population standard deviation σ is known? A)Reject H₀ if z < −2.33 B)Reject H₀ if z < −2.58 C)Reject H₀ if z > 2.33 D)Reject H₀ if z > 2.58

Accepted Answer

Since the owner wants to determine if the mean age is over 35, this is a one-tailed test. For a 99% confidence level in a one-tailed test, the critical z-value is 2.33. Therefore, the rejection region for the hypothesis that the mean age is over 35 would be if the calculated z-value is greater than 2.33.

Question 16

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the: A)significance level. B)critical value. C)test statistic. D)parameter.

Accepted Answer

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the test statistic. The significance level and critical value are used in determining the rejection criteria, but the actual decision to reject or not is based on the value of the test statistic. The parameter is a characteristic of the population being studied and is typically unknown.

Question 17

You reject H₀ if the p-value of your hypothesis is ____________________ than the significance level.

Accepted Answer

The answer of You reject H₀ if the p-value of...

Question 18

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

Accepted Answer

The answer of The probability of a test statistic falling...

Question 19

The ____________________ is a measure of the amount of statistical evidence that supports the alternative hypothesis.

Accepted Answer

The answer of The ____________________ is a measure of the...

Question 20

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample,given that H₀ is true.

Accepted Answer

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

Quiz 11: Introduction to Hypothesis Testing

The rejection region for testing H₀: μ = 100 vs.H₁: μ ≠ 100,at the 0.05 level of significance is:

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:

We have created a 95% confidence interval for μ with the results (10,25) .What conclusion will we make if we test H₀: μ = 26 vs.H₁: μ ≠ 26 at α = 0.025?

The ____________________ is a range of values such that if the test statistic falls into that range we reject the null hypothesis in favor of the alternative hypothesis.

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the ____________________ method.The other approach is the p-value method.

The rejection region for testing H₀: μ = 80 vs.H₁: μ < 80,at the 0.10 level of significance is:

When a null hypothesis is rejected,the test is said to be statistically ____________________ at level α.

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

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the rejection region method.The other approach is the ____________________ method.

If the conclusion of a hypothesis test is that a statistically significant result was found,then the null hypothesis ____________________ (was/was not)rejected.

We have created a 90% confidence interval for μ with the result (25,32) .What conclusion will we make if we test H₀: μ = 28 vs.H₁: μ ≠ 28 at α = 0.10?

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if:

If the p value is less than α in a two-tail test:

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the:

You reject H₀ if the p-value of your hypothesis is ____________________ than the significance level.

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

The ____________________ is a measure of the amount of statistical evidence that supports the alternative hypothesis.

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample,given that H₀ is true.

Quiz 11: Introduction to Hypothesis Testing

The rejection region for testing H0: μ = 100 vs.H1: μ ≠ 100,at the 0.05 level of significance is:

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:

We have created a 95% confidence interval for μ with the results (10,25) .What conclusion will we make if we test H0: μ = 26 vs.H1: μ ≠ 26 at α = 0.025?

The ____________________ is a range of values such that if the test statistic falls into that range we reject the null hypothesis in favor of the alternative hypothesis.

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the ____________________ method.The other approach is the p-value method.

The rejection region for testing H0: μ = 80 vs.H1: μ < 80,at the 0.10 level of significance is:

When a null hypothesis is rejected,the test is said to be statistically ____________________ at level α.

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

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the rejection region method.The other approach is the ____________________ method.

If the conclusion of a hypothesis test is that a statistically significant result was found,then the null hypothesis ____________________ (was/was not)rejected.

We have created a 90% confidence interval for μ with the result (25,32) .What conclusion will we make if we test H0: μ = 28 vs.H1: μ ≠ 28 at α = 0.10?

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if:

If the p value is less than α in a two-tail test:

The numerical quantity computed from the data that is used in deciding whether to reject H0 is the:

You reject H0 if the p-value of your hypothesis is ____________________ than the significance level.

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

The ____________________ is a measure of the amount of statistical evidence that supports the alternative hypothesis.

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample,given that H0 is true.

The rejection region for testing H₀: μ = 100 vs.H₁: μ ≠ 100,at the 0.05 level of significance is:

We have created a 95% confidence interval for μ with the results (10,25) .What conclusion will we make if we test H₀: μ = 26 vs.H₁: μ ≠ 26 at α = 0.025?

The rejection region for testing H₀: μ = 80 vs.H₁: μ < 80,at the 0.10 level of significance is:

We have created a 90% confidence interval for μ with the result (25,32) .What conclusion will we make if we test H₀: μ = 28 vs.H₁: μ ≠ 28 at α = 0.10?

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the:

You reject H₀ if the p-value of your hypothesis is ____________________ than the significance level.

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample,given that H₀ is true.