Ch. 11.2 (Math 241) Part 4 PDF

Preview

Summary

Professor: Ken Li...

Description

Hypothesis Testing on the TI-84 PLUS  The 2-PropZTest command will perform a hypothesis test for the difference between proportions. This command is accessed by pressing STAT and highlighting the TESTS menu.  We enter the values of x 1 , n1 , x 2 , and n2 .

Example (TI-84 PLUS)  The General Social Survey took a poll that asked 350 employed people aged 25–40 whether they used a computer at work, and 259 said they did. They also asked the same question of 500 employed people aged 41–65, and 384 of them said that they used a computer at work. Can you conclude that the proportion of people who use a computer at work is greater among those aged 41–65 than among those aged 25–40? Use the α = 0.05 level.  Solution: We first check the assumptions. We have two independent random samples, and the populations are more than 20 times as large as the samples. The individuals in each sample are divided into two categories with more than 10 individuals in each category. The assumptions are satisfied. We summarize the relevant information:  The null and alternate hypotheses are: H 0 : p 1=p 2 o H 1 : p1 < p2 o 25-40

41-65

Sample size

n1=350

n2=500

Number of individuals

x 1=259

x 2=384

Population proportion

p1

p2

(unknown)

Example (TI-84 PLUS) Press STAT and highlight the TESTS menu and select 2-PropZTest. We enter the following information:

(unknown)

25-40

41-65

Sample size

n1=350

n2=500

Number of individuals

x 1=259

x 2=384

Since we have a left-tailed test, select the ¿ p 2 option. Select Calculate. The P-value is 0.1746. Since P > 0.05, we do not reject H 0 at the α = 0.05 level. We cannot conclude that the proportion of workers aged 41–65 who use a computer at work is greater than the proportion among those aged 25–40....