Question 1

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

Accepted Answer

The level of significance of a test is the significance level or alpha level, which represents the probability of rejecting the null hypothesis when it is actually true, also known as a type I error. Therefore, the level of significance is equal to the probability of making a type I error, given that the null hypothesis is true.

Question 2

is called the observed significance level.

Accepted Answer

False

Question 3

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

Accepted Answer

This is because a small P-value indicates that the probability of obtaining the observed sample data assuming the null hypothesis is true is very low, and therefore it is more likely that the null hypothesis is incorrect.

Question 4

The choice of the alternative hypothesis depends on the objectives of the study.

Accepted Answer

The alternative hypothesis is formulated based on the research question and the objectives of the study. It should be the opposite of the null hypothesis and reflect what the researcher wants to explore or establish through the study. The choice of the alternative hypothesis should be carefully considered to ensure that it aligns with the research objectives and can be tested appropriately.

Question 5

In cities and towns on the borders between states there is a significant amount of flight across state lines to avoid high state taxes on gasoline.Some states (such as Iowa) have large rivers for borders and tolls to cross the bridges.Do these tolls impede traffic to other states to get cheaper gasoline? To test this hypothesis, an experimental Toll-Free Week will be instituted at the Farmington Bridge, where currently 50 cars per day drive out of the state.Let m denote the true average number of border crossings per day at Farmington if there were no toll. a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

The answer of In cities and towns on the borders...

Question 6

a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

The answer of  a)What is the appropriate null hypothesis?...

Question 7

Explain in your own words the distinction between a null and alternative hypothesis.

Accepted Answer

The answer of Explain in your own words the distinction...

Question 8

Psychologists have noted that people tend make classifications based on their "typicality." For example, a dog is more readily classified as a mammal than is a whale, because dogs are "more typical" of mammals than are whales.Previous large- scale studies have established the following for songbirds such as robins: when young children are shown a picture of a songbird and asked if it is a bird they respond "yes" in an average of 750 milliseconds.Do children regard chickens as representative of birds? If so, are they more representative or less representative of birds than are songbirds? Let m represent the mean time it takes children to respond to a question about whether a chicken is a bird.The investigators wish to determine whether the classification time differs from the time needed to classify songbirds. a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

The answer of Psychologists have noted that people tend make...

Question 9

Explain in your own words the distinction between a null and alternative hypothesis.

Accepted Answer

The answer of Explain in your own words the distinction...

Question 10

The Environmental Protection Agency (EPA)is charged with monitoring the environment.One aspect of this is keeping track of "acid rain," a broad term describing the fall of water through an acidic atmosphere.Acidity is measured on the pH scale, where pure water has a pH of 7.0.Normal rain is slightly acidic because carbon dioxide dissolves into it, and thus has a pH of about 5.5.(A lower pH indicates greater acidity.)Suppose the EPA wishes to determine whether a particular area is subject to acid rain.Let m denote the true average for pH in this area. a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

The answer of The Environmental Protection Agency (EPA)is charged with...

Question 11

A type II error is made by failing to reject a false null hypothesis.

Accepted Answer

This is correct. A type II error occurs when we fail to reject a null hypothesis that is actually false, meaning we accept the null hypothesis when in reality the alternative hypothesis is true.

Question 12

All other things being equal, choosing a smaller value of  will increase the probability of making a type II error.

Accepted Answer

Choosing a smaller value of 11eb9097_a05e_543a_854a_c1e08b78aeaa_TB8803_11 means having a higher acceptance region and a lower rejection region, which can increase the probability of failing to reject a false null hypothesis, leading to a type II error.

Question 13

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than

Accepted Answer

The conventional threshold for statistical significance is a P-value less than or equal to 0.05 (or 5%).

Question 14

For tests of hypotheses about  decreases as the sample size increases if the level of significance stays the same.

Accepted Answer

The answer of For tests of hypotheses about  decreases...

Question 15

Explain in your own words what a hypothesis test is.

Accepted Answer

The answer of Explain in your own words what a...

Question 16

The power of a test is the probability of failing to reject the null hypothesis.

Accepted Answer

The power of a test is the probability of correctly rejecting the null hypothesis, not the probability of failing to reject it.

Question 17

The statement  = 100 is a statistical hypothesis.

Accepted Answer

The given statement does not resemble a statistical hypothesis as it is simply a random string of alphanumeric characters followed by an equal sign and a number. A statistical hypothesis typically involves a claim or assumption about a population parameter that can be tested using statistical methods.

Question 18

Explain in your own words what a hypothesis test is.

Accepted Answer

The answer of Explain in your own words what a...

Question 19

If the null hypothesis is not rejected, there is strong statistical evidence that thenull hypothesis is true.

Accepted Answer

If the null hypothesis is not rejected, it does not necessarily mean that the null hypothesis is true. It means that there is not enough evidence to reject the null hypothesis. There could be other factors at play, such as low statistical power, that prevent the rejection of the null hypothesis. Therefore, we cannot conclude that the null hypothesis is true based solely on the failure to reject it.

Quiz 10: Hypothesis Testing Using a Single Sample

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

is called the observed significance level.

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

The choice of the alternative hypothesis depends on the objectives of the study.

a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

Explain in your own words the distinction between a null and alternative hypothesis.

Explain in your own words the distinction between a null and alternative hypothesis.

A type II error is made by failing to reject a false null hypothesis.

All other things being equal, choosing a smaller value of will increase the probability of making a type II error.

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than

For tests of hypotheses about decreases as the sample size increases if the level of significance stays the same.

Explain in your own words what a hypothesis test is.

The power of a test is the probability of failing to reject the null hypothesis.

The statement = 100 is a statistical hypothesis.

Explain in your own words what a hypothesis test is.

If the null hypothesis is not rejected, there is strong statistical evidence that thenull hypothesis is true.