# 11. More about Hypothesis Testing Flashcards

1
Q

Two-Tailed or Nondirectional Test

A

Rejection regions are located in both tails of the sampling distribution.

2
Q

One-Tailed or Directional Test

A

Rejection region is located in just one tail of the sampling distribution.

3
Q

The following statement could represent the point of departure for a hypothesis test. Given only the information in the statement, would you use a two-tailed (or nondirectional) test, a one-tailed (or directional) test with the lower tail critical, or a one-tailed (or directional) test with the upper tail critical?
Indicate your decision by specifying the appropriate H0 and H1. Furthermore, whenever you conclude that the test is one-tailed, indicate the precise word (or words) in the statement that justifies the one-tailed test.

An investigator wishes to determine whether, for a sample of drug adicts, the mean score on the depression scale of a personality test differs from a score of 60, which, according to the test documentation, represents the mean score for the general population.

A

H0: µ = 60

H1: µ ≠ 60

4
Q

The following statement could represent the point of departure for a hypothesis test. Given only the information in the statement, would you use a two-tailed (or nondirectional) test, a one-tailed (or directional) test with the lower tail critical, or a one-tailed (or directional) test with the upper tail critical?
Indicate your decision by specifying the appropriate H0 and H1. Furthermore, whenever you conclude that the test is one-tailed, indicate the precise word (or words) in the statement that justifies the one-tailed test.

To increase rainfall, extensive cloud-seeding experiments are to be concluded, and the results are to be compared with a baseline figure of 0.54 inch of rainfall (for comparable periods when cloud seeding was not done).

A

H0: µ ≤ 0.54

H1: µ > 0.54

Justification: to increase rainfall

5
Q

The following statement could represent the point of departure for a hypothesis test. Given only the information in the statement, would you use a two-tailed (or nondirectional) test, a one-tailed (or directional) test with the lower tail critical, or a one-tailed (or directional) test with the upper tail critical?
Indicate your decision by specifying the appropriate H0 and H1. Furthermore, whenever you conclude that the test is one-tailed, indicate the precise word (or words) in the statement that justifies the one-tailed test.

Public health statistics indicate, we will assume, that American males gain an average of 23 lbs during the 20-year period after age 40. An ambitious weight-reduction program, spanning 20 years, is being tests with a sample of 40 year-old men.

A

H0: µ ≥ 23

H1: µ < 23

Justification: weight-reduction program

6
Q

The following statement could represent the point of departure for a hypothesis test. Given only the information in the statement, would you use a two-tailed (or nondirectional) test, a one-tailed (or directional) test with the lower tail critical, or a one-tailed (or directional) test with the upper tail critical?
Indicate your decision by specifying the appropriate H0 and H1. Furthermore, whenever you conclude that the test is one-tailed, indicate the precise word (or words) in the statement that justifies the one-tailed test.

When untreated during their lifetime, cancer-susceptible mice have an average life span of 134 days. To determine the effects of a potentially life-prolonging (and cancer-retarding) drug, the average life span is determined for a group of mice that receives this drug.

A

H0: µ ≤ 134

H1: µ > 134

Justification: life-prolonging drug

7
Q

Should H0 be retained or rejected?

Given a one-tailed test, lower tail critical with α = .01 and z = –2.34

A

Reject H0 at the .01 level of significance because z = –2.34 is more negative than –2.34.

8
Q

Should H0 be retained or rejected?

Given a one-tailed test, lower tail critical with α = .01 and z = –5.13

A

Reject H0 at the .01 level of significance because z = –5.13 is more negative than –2.33.

9
Q

Should H0 be retained or rejected?

Given a one-tailed test, lower tail critical with α = .01 and z = 4.04

A

Retain H0 at the .01 level of significance because z = 4.04 is less negative than –2.33.

(The value of the observed z is in the direction of no concern.)

10
Q

Should H0 be retained or rejected?

Given a one-tailed test, uppertail critical with α = .05 and z = 2.00

A

Reject H0 at the .05 level of significance because z = 2.00 is more positive than 1.65.

11
Q

Should H0 be retained or rejected?

Given a one-tailed test, uppertail critical with α = .05 and z = –1.80

A

Retain H0 at the .05 level of significance because z = –1.80 is less positive than 1.65.

(The value of the observed z is in the direction of no concern.)

12
Q

Should H0 be retained or rejected?

Given a one-tailed test, uppertail critical with α = .05 and z = 1.61

A

Retain H0 at the .05 level of significance because z = 1.61 is less positive than 1.65.

13
Q

Specify the decision rule for the following situation:

a two-tailed test with α = .05

A

Reject H0 at the .05 level of significance if z equals or is more positive than 1.96 or if z equals or is more negative than –1.96.

14
Q

Specify the decision rule for the following situation:

a one-tailed test, upper tail critical, with α = .01

A

Reject H0 at the .01 level of significance if z equals or is more positive than 2.33.

15
Q

Specify the decision rule for the following situation:

a one-tailed test, lower tail critical, with α = .05

A

Reject H0 at the .05 level of significance if z equals or is more negative than –1.65.

16
Q

Specify the decision rule for the following situation:

a two-tailed test with α = .01

A

Reject H0 at the .01 level of significance if z equals or is more positive than 2.58 or if z equals or is more negative than –2.58.

17
Q

Type I Error

A

Rejecting a true null hypothesis.

18
Q

Type II Error

A

Retaining a false null hypothesis.

19
Q

List the four possible outcomes for any hypothesis.

A

Correct decision (True H0 is retained)

Type I Error

Correct decision (False H0 is rejected)

Type II Error

20
Q

Under the U.S. Criminal Code, a defendant is presumed innocent until proven guilty. Viewing a criminal trial as a hypothesis test (with H0 specifying that the defendant is innocent), describe each of the four possible outcomes.

A

Correct Decision: Innocent defendant is released

Type I Error: Innocent defendant is sentenced (False Alarm).

Correct Decision: Guilty defendant is sentenced

Type II Error: Guilty defendant is released (Miss)

21
Q

Alpha (α)

A

The probability of a type I error, that is, the probability of rejecting a true null hypothesis.

22
Q

In order to eliminate the type I error, someone decides to use the .00 level of significance. What’s wrong with this procedure?

A

A false H0 will never be rejected.

23
Q

Effect

A

Any difference between a true and a hypothesized population mean.

24
Q

Hypothesized Sampling Distribution

A

Centered about the hypothesized population mean, this distribution is used to generate the decision rule.

25
Q

True Sampling Distribution

A

Centered about the true population mean, this distribution produces the one observed mean (or z).

26
Q

Beta (β)

A

The probability of a type II error, that is, the probability of retaining a false null hypothesis.

27
Q

Comment critically on the following experimental report:

Using a group of 4 subjects, an investigator announces that H0 was retained at the .05 level of significance.

A

Because of the small sample size, only very large effects will be detected.

28
Q

Comment critically on the following experimental report:

Using a group of 600 subjects, an investigator reports that H0 was rejected at the .05 level of significance.

A

Because of the large sample size, even small, unimportant effects will be detected.

29
Q

Power (1 – β)

A

The probability of detecting a particular effect.

30
Q

Power

A

Shows how the likelihood of detecting any possible effect varies for a fixed sample size.

31
Q

An investigator consults a chart to determine the sample size required to detect an eight-point effect with a probability of .80. What happens to this detection rate of .80–will it actually be smaller, the same, or larger–if, unknown to the investigator, the true effect actually equals…

twelve points?

A

The power for the 12-point effect is larger than .80 because the true sampling distribution is shifted further into the rejection region for the false H0.

32
Q

An investigator consults a chart to determine the sample size required to detect an eight-point effect with a probability of .80. What happens to this detection rate of .80–will it actually be smaller, the same, or larger–if, unknown to the investigator, the true effect actually equals…

five points?

A

The power for the 5-point effect is smaller than .80 because the true sampling distribution is shifted further into the retention region for the false H0.