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Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Practice 2: Hypothesis Testing for Two Averages

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 conduct a hypothesis test of two means.

## Given

The U.S. Center for Disease Control reports that the mean 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 mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

## Hypothesis Testing: Two Means

### Exercise 1

Is this a test of means or proportions?

Means

### 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

• 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?

two-tailed

### Exercise 4

What is the Random Variable of interest for this test?

#### Solution

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 of interest for this test.

#### Solution

The difference between the mean life spans of whites and nonwhites.

### Exercise 6

Which distribution (Normal or student's-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.

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 pp size 12{p - {}} {}value.

### Exercise 10

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

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

• a. Reject the null hypothesis

## Discussion Question

### Exercise 12

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

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