15 Errors and Power

Question 1

What is a Type I Error?

Answer 1

Rejecting H0 when it is actually true

Question 2

What is a Type II Error?

Answer 2

Not rejecting H0 when it is actually false

Question 3

The size of a hypothesis test is defined as what?

Answer 3

Actual Significance level

This represents the probability of making a Type I error.

Question 4

In hypothesis testing, what does the power of a test refer to?

Answer 4

Probability of rejecting H0 when it is not true

Question 5

What is the formula used to calculate power?

Answer 5

Power = 1 – P(Type II error).

Question 6

What is the relationship between sample size and the probability of a Type II error?

Answer 6

Larger sample size decreases probability of Type II error

Increasing sample size increases the power of the test.

Question 7

In the context of hypothesis testing, what is a critical region?

Answer 7

The set of values that leads to rejection of H0

It is determined based on the significance level.

Question 8

What is the significance level in hypothesis testing?

Answer 8

The probability of making a Type I error

Question 9

What is the p-value method used for in hypothesis testing?

Answer 9

To determine the significance of the test statistic

It compares the p-value to the significance level to decide on H0.

Question 10

What is the critical value in hypothesis testing?

Answer 10

The threshold that determines the critical region

It is based on the significance level and the distribution of the test statistic.

Question 11

True or false: A Type I error occurs when a true null hypothesis is accepted.

Answer 11

FALSE

A Type I error occurs when a true null hypothesis is rejected.

Question 12

What is the probability of making a Type I error at a 5% significance level?

Answer 12

0.05 for a continuus hypthesis test
0.05 or smaller for a discrete test

This means there is a 5% (or lower) chance of incorrectly rejecting the null hypothesis.

Question 13

What is the probability of making a Type II error dependent on?

Answer 13

The true/new parameter

It requires knowledge of the actual parameter to calculate.

Question 14

What is the null hypothesis (H0)?

Answer 14

The hypothesis that there is no effect or difference

It is the default assumption in hypothesis testing.

Question 15

What is the alternative hypothesis (H1)?

Answer 15

The hypothesis that there is an effect or difference

It is what researchers aim to support through testing.

Question 16

What does not sufficient evidence mean in hypothesis testing?

Answer 16

Not enough data to reject H0

This leads to a failure to find statistical significance.

Question 17

What does significant mean in the context of hypothesis testing?

Answer 17

H0 has been rejected as the results are unlikely to have occurred by chance

Typically associated with a p-value less than the significance level.

Question 18

What is the Central Limit Theorem?

Answer 18

• for samples which are large (𝑛 ≥ 30)
• if the underlying data is not normally distributed
• then we can approximate the sample mean distribution

Question 19

In hypothesis testing, the critical region is chosen to be _______.

Answer 19

The area where the null hypothesis is rejected

This region is determined based on the significance level of the test.

Question 20

Define p-value.

Answer 20

A statistical measure that represents the probability of obtaining results as extreme as, or more extreme than, the test statistic observed in a study, assuming the null hypothesis is true

It quantifies the strength of evidence against the null hypothesis.

Question 21

True or false: The p-value in a one-tailed test is equal to the probability of being less extreme than the test statistic.

Answer 21

FALSE

In a one-tailed test, the p-value is the probability of being more extreme than the test statistic.

Question 22

What is a critical value?

Answer 22

A point on the test statistic’s distribution that defines the threshold for rejecting the null hypothesis

It helps determine whether the observed data is significant.

Question 23

What is the main difference between p-value and critical value?

Answer 23

• p-value quantifies evidence against the null hypothesis
• Critical value sets a threshold for significance

Both are used in hypothesis testing but serve different roles.

Question 24

What do lower p-values suggest?

Answer 24

The null hypothesis should be rejected

When p is low, reject H0

Question 25

What do **critical values** determine?

Answer 25

Whether the null hypothesis should be rejected or not ## Footnote Results that exceed the critical value support adopting the alternative hypothesis.

Question 26

What is the **similarity** between p-values and critical values?

Answer 26

Both are used to determine if observed data provides enough evidence to reject the null hypothesis ## Footnote They play a crucial role in hypothesis testing.

Question 27

How is the probability of a Tyle II error calculated?

Answer 27

P(Being in the **not** rejection region|a new parameter)