Hypothesis Testing for Proportions

 These are the Bluman 5 th McGraw Hill… Edition slides ©  Edited by Darton State U. / Cordele staff to demonstrate the TI-84 1-PropZTest and p-value method

1

Bluman, Chapter 8

Example 8-17: Avoiding Trans Fats A 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.

H

0 :

p =

0.60 (claim) and

H

1 :

p

 0.60

.

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Bluman, Chapter 8

Example 8-17: Avoiding Trans Fats A 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?

Steps 2 & 3: Compute the test value and the p value .

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Bluman, Chapter 8

Example 8-17: Avoiding Trans Fats

Step 4: Make the decision.

Do not reject the null hypothesis

since the p-value of 0.248 is NOT < the level of significance,

𝜶 =. 𝟎𝟓

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.

Bluman, Chapter 8

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Example 8-18: Call-Waiting Service A telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 150 customers and found that 30% had call waiting. At

α

= 0.05

, is there enough evidence to reject the claim?

Step 1: State the hypotheses and identify the claim.

H

0 :

p =

0.40 (claim) and

H

1 :

p

 0.40

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Bluman, Chapter 8

Careful Reading and TI-84 Input

 The calculator asks for n.

IT’S NOT 30!!!!

 It’s “30% of 150”, that’s how many  You can type 0.30*150 at the n= prompt and let the calculator figure out that it’s 45.

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Bluman, Chapter 8

Example 8-18: Call-Waiting Service A telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 150 customers and found that 30% had call waiting. At

α

= 0.05

, is there enough evidence to reject the claim?

Steps 2/3: Compute the test value and the p value.

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Bluman, Chapter 8

Example 8-18: Call-Waiting Service

Step 4: Make the decision.

Reject the null hypothesis since the p value of .012

IS < the level of significance,

𝒂 =. 𝟎𝟓

Step 5: Summarize the results.

There is enough evidence to reject the claim that 40% of the telephone company’s customers have call waiting.

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Bluman, Chapter 8