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Hypothesis Testing: Two Population Means and Two Population Proportions: Practice 2

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: This module provides a practice of Hypothesis Testing: Two Population Means and Two Population Proportions: as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student Learning Outcome

  • The student will explore the properties of hypothesis testing with two averages.

Given

The U.S. Center for Disease Control reports that the average life expectancy for whites born in 1900 was 47.6 years and for nonwhites it was 33.0 years. (http://www.cdc.gov/nchs/data/dvs/nvsr53_06t12.pdf ) Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the average life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the average life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the average life spans in the county were the same for whites and nonwhites.

Hypothesis Testing: Two Averages

Exercise 1

Is this a test of averages or proportions?

Solution 1

Averages

Exercise 2

State the null and alternative hypotheses.

  • a. H0:H0: size 12{H rSub { size 8{0} } :} {}
  • b. Ha:Ha: size 12{H rSub { size 8{a} } :} {}

Solution 2

  • a. H 0 : μ W = μ NW H 0 : μ W = μ NW size 12{H rSub { size 8{O} } :μ rSub { size 8{W} } =μ rSub { size 8{ ital "NW"} } } {}
  • b. H a : μ W ≠ μ NW H a : μ W ≠ μ NW size 12{H rSub { size 8{a} } :μ rSub { size 8{W} } <> μ rSub { size 8{ ital "NW"} } } {}

Exercise 3

Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

Solution 3

two-tailed

Exercise 4

What is the Random Variable of interest for this test?

Solution 4

X ¯ W − X ¯ NW X ¯ W − X ¯ NW size 12{ {overline {X}} rSub { size 8{W} } - {overline {X}} rSub { size 8{ ital "NW"} } } {}

Exercise 5

In words, define the Random Variable for this test.

Solution 5

student-t

Exercise 6

Which distribution (Normal or student-t) would you use for this hypothesis test?

Exercise 7

Explain why you chose the distribution you did for the above question.

Exercise 8

Calculate the test statistic.

Solution 8

5.42

Exercise 9

Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p−p− size 12{p - {}} {}value.

Figure 1
Figure 1 (9.png)

Exercise 10

Find the p−p− size 12{p - {}} {}value:

Solution 10

0.0000

Exercise 11

At a pre-conceived α=0.05α=0.05 size 12{α=0 "." "05"} {}, what is your:

  • a. Decision:
  • b. Reason for the decision:
  • c. Conclusion (write out in a complete sentence):

Solution 11

  • a. Reject the null hypothesis

Discussion Question

Exercise 12

Does it appear that the averages are the same? Why or why not?

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