Chapter 8 test

Test on Chapter 8 will be on:

Feb 21, 2014

Bluman, Chapter 8 1

Review: Concepts and Symbols

p = population proportion

(read p “hat”) = sample proportion

For a sample proportion,

where X = number of sample units that possess the characteristics of interest and n = sample size.

Bluman, Chapter 7 2

p̂

ˆ ˆ ˆ ˆand 1

X n X

p q or q pn n

Sec 8.4

Z Test for a Proportion

Bluman, Chapter 7 3

8.4 z Test for a Proportion

Since a normal distribution can be used to approximate the binomial distribution when np 5 and nq 5, the standard normal distribution can be used to test hypotheses for proportions.

The formula for the z test for a proportion is

where

Bluman, Chapter 8 4

ˆ p p

zpq n

ˆ sample proportion

population proportion

sample size

Xp

np

n

Chapter 8Hypothesis Testingthe traditional method

Section 8-4Example 8-17

Page #438

Bluman, Chapter 8 5

Example 8-17: Avoiding Trans FatsA dietitian claims that 60% of people are trying to avoid trans fats in their diets. She randomly selected 200 people and found that 128 people stated that they were trying to avoid trans fats in their diets. At α = 0.05, is there enough evidence to reject the dietitian’s claim?

Step 1: State the hypotheses and identify the claim.

H0: p = 0.60 (claim) and H1: p 0.60

Step 2: Find the critical value.

Since α = 0.05 and the test is a two-tailed test, the critical value is z = ±1.96.

Bluman, Chapter 8 6

Example 8-17: Avoiding Trans FatsA dietitian claims that 60% of people are trying to avoid trans fats in their diets. She randomly selected 200 people and found that 128 people stated that they were trying to avoid trans fats in their diets. At α = 0.05, is there enough evidence to reject the dietitian’s claim?

Step 3: Compute the test value.

Bluman, Chapter 8 7

ˆ p p

zpq n

0.64 0.60

0.60 0.40 200

1.15

128ˆ 0.64

200 X

pn

Step 4: Make the decision.Do not reject the null hypothesis since the test value falls outside the critical region.

Step 5: Summarize the results.

There is not enough evidence to reject the claim that 60% of people are trying to avoid trans fats in their diets.

Example 8-17: Avoiding Trans Fats

Bluman, Chapter 8 8

Chapter 8Hypothesis Testing

Section 8-4Example 8-18

Page #439

Bluman, Chapter 8 9

Example 8-18: Call-Waiting ServiceA telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 100 customers and found that 37% had call waiting. At α = 0.01, is there enough evidence to reject the claim?

Step 1: State the hypotheses and identify the claim.

H0: p = 0.40 (claim) and H1: p 0.40

Step 2: Find the critical value.

Since α = 0.01 and the test is a two-tailed test, the critical value is z = ±2.58.

Bluman, Chapter 8 10

Example 8-18: Call-Waiting ServiceA telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 100 customers and found that 37% had call waiting. At α = 0.01, is there enough evidence to reject the claim?

Step 3: Compute the test value.

Bluman, Chapter 8 11

ˆ p p

zpq n

0.37 0.40

0.40 0.60 100

0.61

Step 4: Make the decision.Do not reject the null hypothesis since the test value falls outside the critical region.

Step 5: Summarize the results.

There is not enough evidence to reject the claim that 40% of the telephone company’s customers have call waiting.

Example 8-18: Call-Waiting Service

Bluman, Chapter 8 12

On your Own

Calculator Instructions:

Page 444

Sec 8.4

Page 442 #1-5 all, 7,13, 16, 17

Bluman, Chapter 8 13