Free Printable Type I and II errors/Power

1.

In a type 1 error...

a)

the null is true but we reject it

b)

the null is true and we fail to reject it

c)

the null is false and we reject it

d)

the null is false but we fail to reject it

2.

An experiment is conducted to determine whether a new treatment helps patients with diabetes.

H0: The treatment does not work.

Ha: The treatment works.

Which of the following is a Type I Error in this situation?

a)

the treatment does not work, but we believe that it does

b)

the treatment does not work, and we believe it does not work

c)

the treatment works, and we believe that it works

d)

the treatment works, but we think that it doesn't

3.

An experiment is conducted to determine whether a new treatment helps patients with diabetes.

H0: The treatment does not work.

Ha: The treatment works.

Which of the following is a Type II Error in this situation?

a)

the treatment does not work, but we believe that it does

b)

the treatment does not work, and we believe it does not work

c)

the treatment works, and we believe that it works

d)

the treatment works, but we think that it doesn't

4.

A researcher plans to conduct a test of hypotheses at the α = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is

a)

0.01

b)

0.10

c)

0.90

d)

0.99

5.

When leaving for school, you make a judgement on these hypotheses. H_o: The weather will remain dry. H_a: It will rain. What are the results of the Type I and Type II errors?

a)

Type I: Needlessly carry around an umbrella all day. Type II: Get drenched

b)

Type I: Get drenched. Type II: Needlessly carry around an umbrella all day

c)

Type I: Carry umbrella & it rains. Type II: Carry no umbrella & it doesn't rain

d)

Type I: Get drenched. Type II: Carry umbrella & it rains

6.

Because of the expense of running a campaign, a potential candidate will only run if there is more than 40% initial support for him. To test this they take a SRS of 200 voters and ask if they would vote for him. They run a significance test with H₀: p = 0.40 vs. H_a: p > 0.40. Which of the following describes a consequence of Type II error in this setting?

a)

Thinking that there is enough support, but the candidate still decides not to run for office.

b)

Thinking that there is not enough support, but the candidate still decides to run for office.

c)

Thinking that there is not enough support, so the candidate decides not to run for office. The candidate saves money, but might have won because the initial support is more than 40%

d)

Thinking that there is enough support, so the candidate decides to run for office. This is a waste of money because the initial support is not more than 40%.

7.

A type I error involves a researcher wrongly accepting which hypothesis?

a)

Alternative

b)

Null

8.

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:

$H_0:\ p\ =\ 0.09$ $H_a:\ p\ \ne0.09$

Which of the following would be a type I error?

a)

She concludes the town's unemployment rate is not 9% when it actually is.

b)

She concludes the town's unemployment rate is not 9% when it actually is not.

c)

She concludes the town's unemployment rate is 9% when it actually is.

d)

She concludes the town's unemployment rate is 9% when it actually is not.

9.

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:

$H_0:\ p\ =\ 0.09$ $H_a:\ p\ \ne0.09$

Which of the following would be a type II error?

a)

She concludes the town's unemployment rate is not 9% when it actually is.

b)

She concludes the town's unemployment rate is not 9% when it actually is not.

c)

She concludes the town's unemployment rate is 9% when it actually is.

d)

She concludes the town's unemployment rate is 9% when it actually is not.

10.

Regulations from the EPA say that soil used in playgrounds should not have lead levels more than 400 ppm. Before beginning construction on a new site, a sample of soil is taken and tested. If the mean level of lead in this soil is significantly higher than 400 ppm, then construction cannot continue. Here are the hypotheses:

$H_0:\ \mu\ =\ 400\ ppm$ $H_a:\ \mu\ >\ 400\ ppm$

Which of the following would be a type II error?

a)

The soil is actually safe and construction continues

b)

The soil is actually safe and construction stops

c)

The soil is actually unsafe and construction continues

d)

The soil is actually unsafe and construction stops

11.

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this is true for her town, so she plans to take a sample of residents to see if the unemployment rate is significantly different than 9% in her town. Here are the hypotheses:

$H_0:\ p\ =\ 0.09$ $H_a:\ p\ \ne0.09$

Which of the following would be a type I error?

a)

She concludes the town's unemployment rate is not 9% when it actually is.

b)

She concludes the town's unemployment rate is not 9% when it actually is not.

c)

She concludes the town's unemployment rate is 9% when it actually is.

d)

She concludes the town's unemployment rate is 9% when it actually is not.

12.

What is the probability of making a Type I error?

a)

alpha

b)

1 minus the probability of a Type II error

c)

1 minus the power

d)

the p-value

13.

In a Type 2 error...

a)

the null is true but we reject it

b)

the null is true and we fail to reject it

c)

the null is false and we reject it

d)

the null is false but we fail to reject it

14.

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested is higher than 40%, in which case they would consider building the new cafeteria. Here are the hypotheses they'll use:

H0: p = 0.40, Ha: p > 0.40

In a Type (a) error, the university will not build a new cafeteria when the students want it.

Type I and II errors/Power

Total questions: 14

Worksheet time: 10mins

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