Exam 10: Hypothesis Testing Using a Single Sample

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

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.

Explain in your own words what a hypothesis test is.

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

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

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

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

The statement = 100 is a statistical hypothesis.

Explain in your own words what a hypothesis test is.

is called the observed significance level.

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.

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.

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.

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

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

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

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

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