Unit 8 - Significance Tests

Question 1

MUST KNOW: What is a significance test?

Answer 1

A significance test is a formal procedure for using observed data to decide between two competing claims (hypotheses).

Question 2

MUST KNOW: What is the null hypothesis?

Answer 2

The null hypothesis is the claim we weight evidence against in a statistical test. It is a statement of “no difference.”

Question 3

What is the alternative hypothesis?

Answer 3

The alternative hypothesis is the claim we are trying to find evidence for; it is the claim we suspect to be true instead of the null hypothesis.

Question 4

What form does the null hypothesis take?

Answer 4

H_0: parameter = value

Question 5

What forms do the alternative hypothesis take?

Answer 5

H_a: parameter value
H_a: parameter not equal to value

Question 6

MUST KNOW: What does it mean for an alternative hypothesis to be one sided?

Answer 6

The alternative hypothesis is one sided when it states that the parameter is larger/smaller than the null hypothesis value.

Question 7

MUST KNOW: What does it mean for an alternative hypothesis to be two sided?

Answer 7

The alternative hypothesis is two sided if it states that the parameter is different from the null hypothesis value.

Question 8

MUST MUST MUST KNOW: What is a P-value?

Answer 8

A P-value is the probability, assuming the null hypothesis is true, that the statistic (x-bar or p-hat ̂) would take a value as extreme or more extreme than the one actually observed (in the direction specified by H_a)

Question 9

What is a significance level?

Answer 9

A significance level is a fixed value that we compare a P-value to to determine whether we should reject the null hypothesis.

Question 10

What is the most common significance level?

Answer 10

Alpha = 0.05

Question 11

MUST KNOW: What does it mean for results to be statistically significant?

Answer 11

The outcome will rarely occur by chance alone.

Question 12

What must be true about a P-value for results to be statistically significant?

Answer 12

When the P-value is less than alpha, results are statistically significant (when we reject the null hypothesis).

If no significance level is given, use 0.05; in other words, results are statistically significant if the P-value is less than 0.05.

Question 13

MUST KNOW: When the P-value is less than alpha, what conclusion will you draw in your significance test?

Answer 13

Reject the null hypothesis

Question 14

MUST KNOW: When the P-value is greater than or equal to than alpha, what conclusion will you draw in your significance test?

Answer 14

Fail to reject the null hypothesis

Question 15

MUST KNOW: What is a Type I error?

Answer 15

Reject the null hypothesis when the null hypothesis is true.

Question 16

MUST KNOW: What is a Type II error?

Answer 16

Fail to reject the null hypothesis when the alternative hypothesis is true.

Question 17

What kind of error can we make when we reject the null hypothesis?

Answer 17

Type I

Question 18

What kind of error can we make when we fail to reject the null hypothesis?

Answer 18

Type II

Question 19

What kind of error can we make when the P-value is less than alpha?

Answer 19

Type I

Question 20

What kind of error can we make when the P-value is greater than alpha?

Answer 20

Type II

Question 21

The P-value of a one-sided test is 0.08. What would the P-value be if this test were two-sided?

Answer 21

0.16

Question 22

The P-value of a two-sided test is 0.22. What would the P-value be if this test were one-sided?

Answer 22

0.11

Question 23

MUST KNOW: What is an advantage to confidence intervals over significance tests?

Answer 23

Confidence intervals provide more information because they provide a set of plausible values for a parameter, whereas a significance test only tells you whether we have evidence for or against the null hypothesis.

Question 24

MUST KNOW: Fill in the blanks:
A \_\_\_\_\_\_\_ (one/two sided) significance test at a 0.05 significance level gives the same conclusion as constructing a \_\_\_\_\_\_\_\_\_ confidence interval.

Answer 24

A TWO SIDED significance test at a 0.05 significance level gives the same conclusion as constructing a 95% confidence interval.

Question 25

Fill in the blanks:

A two-sided ________________ at a _____ significance level gives the same conclusion as constructing a 99% __________.

Answer 25

A two-sided SIGNIFICANCE TEST at a 0.01 significance level gives the same conclusion as constructing a 99% CONFIDENCE INTERVAL.

Question 26

What is the general form of a standardized test statistic?

Answer 26

(statistic - parameter) / standard deviation of statistic

Question 27

A one-sided significance test has a test statistic of z = 1.58. What is the P-value for this test?

Answer 27

P-value: 0.0571

Question 28

A one-sided significance test has a test statistic of z = -2.34. What is the P-value for this test?

Answer 28

P-value: 0.0096

Question 29

A two-sided significance test has a test statistic of z = 2.88. What is the P-value for this test?

Answer 29

P-value: 2(0.0019884417) = 0.00398

Question 30

A two-sided significance test has a test statistic of z = -1.92. What is the P-value for this test?

Answer 30

P-value: 2(0.02742888) = 0.05486

Question 31

MUST KNOW: What information does a test statistic provide?

Answer 31

The test statistic tells how far your sample data is from the null parameter value in standardized units.