# 11. More about Hypothesis Testing Flashcards

Two-Tailed or Nondirectional Test

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

One-Tailed or Directional Test

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

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.

H0: µ = 60

H1: µ ≠ 60

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).

H0: µ ≤ 0.54

H1: µ > 0.54

Justification: to increase rainfall

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.

H0: µ ≥ 23

H1: µ < 23

Justification: weight-reduction program

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.

H0: µ ≤ 134

H1: µ > 134

Justification: life-prolonging drug

Should H0 be retained or rejected?

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

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

Should H0 be retained or rejected?

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

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

Should H0 be retained or rejected?

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

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.)

Should H0 be retained or rejected?

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

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

Should H0 be retained or rejected?

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

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.)

Should H0 be retained or rejected?

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

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

Specify the decision rule for the following situation:

a two-tailed test with α = .05

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.

Specify the decision rule for the following situation:

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

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

Specify the decision rule for the following situation:

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

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