Stats Exam 4.1- Types of Errors

The Ford Motor Company claims that its 2017 model of the Ford Escape averages more than 30 miles per gallon for highway driving. To investigate this claim, which of the following hypotheses is appropriate?

• 𝐻0: 𝜇 > 30 𝑚𝑝𝑔; 𝐻𝐴: 𝜇 < 30 𝑚𝑝𝑔

• 𝐻0: 𝜇 = 30 𝑚𝑝𝑔; 𝐻𝐴: 𝜇 > 30 𝑚𝑝g

• 𝐻0: 𝜇 = 30 𝑚𝑝𝑔; 𝐻𝐴: 𝜇 ≠ 30 𝑚𝑝𝑔

• 𝐻0: 𝜇 > 30 𝑚𝑝𝑔; 𝐻𝐴: 𝜇 = 30 𝑚𝑝𝑔

The power of a test is denoted by:

• 1 – β

• β

• 1 − α

• α

Which of the following is a true statement?

• When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

The value set for  $\alpha$   is known as:

• the rejection level

• the significance level

• the acceptance level

• the error in the hypothesis test

Given H0: µ = 25, Ha: µ ≠ 25, and P-value = 0.041. Do you reject or fail to reject H0 at the 0.01 level of significance?

• fail to reject H0

• not sufficient information to decide

• reject H0

A test to screen for a serious but curable disease is similar to hypothesis testing, with a null hypothesis of

no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be

given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario, it

is better to increase the probability of:

• making a Type 1 error, providing treatment when it is not needed.

• making a Type 1 error, not providing treatment when it is needed.

• making a Type 2 error, providing treatment when it is not needed.

• making a Type 2 error, not providing treatment when it is needed.

Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company who makes Kleenex brand tissues thinks that fewer of their tissues are needed. What are their null and alternative hypotheses?

• H0: µ = 60 vs. HA: µ > 60

• H0: µ = 60 vs. HA: µ < 60

• H0: µ < 60 vs. HA: µ = 60

For a given level of significance α, if the sample size n is increased, the probability of a Type II error β will:

• decrease

• increase

• remain the same

• not enough information to tell

Which of the following is true of the null and alternative hypotheses?

• It is possible for neither hypothesis to be true

• Both hypotheses must be true

• It is possible for both hypotheses to be true

• Exactly one hypothesis must be true

In a hypothesis test:

• the null hypothesis is what we are trying to prove

• the alternate hypothesis is always assumed to be true

• the alternate hypothesis is accepted unless there is sufficient evidence to say otherwise

• the null hypothesis is not rejected unless there is sufficient evidence to reject it.