Hypothesis Testing for Proportion

Testing a Claim about a Proportion Now we put the theory or Hypothesis testing to use testing claims about proportions!

We first need to make sure we meet the requirements.

1. The sample observations are a simple random sample.

2. The conditions for a binomial sample are satisfied.

3. The conditions 𝑛𝑝 ≥ 5 and 𝑛𝑞 ≥ 5 are both satisfied.

Test Statistic for Testing a Claim about a Proportion 𝑝 − 𝑝 𝑧 = 𝑝𝑞 𝑛

Testing a Claim about a Proportion P-value method in 5 Steps 1. State the hypothesis and state the claim. 2. Compute the test value. (Involves find the sample statistic). 3. Draw a picture and find the P-value.

4. Make the decision to reject 𝐻 0 and 𝛼) or not. (compare P-value 5. Summarize the results.

Testing a Claim about a Proportion In a survey, 1864 out of 2246 randomly selected adults in the United States said that texting while driving should be illegal. Consider a hypothesis test that uses a 0.05 significance level to test the claim that more than 80% of adults believe that texting while driving should be illegal.

1.

𝐻 0 : 𝑝 = .8

and 𝐻 1 : 𝑝 > .8

(claim) 1864 2. Note: 𝑝 = = .83 𝑧 = 2246 3. P-value is 0.000196 or 0 𝑝𝑞/ 𝑛 = .83−.8

.8 (.2)/ 𝑛 = 3.544

4. Since 0 < 0.05

(significance level) reject the null.

5. There is sufficient evidence to support the claim that 80% of adults believe that texting should be illegal.

6. Or use [stat] → T est → 1-PropZTest

Testing a Claim about a Proportion In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won. Use a 0.01 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Testing a Claim about a Proportion The company Drug Test Success provides a “1-Panel-THC” test for marijuana usage. Among 300 tested subjects, results from 27 subjects were wrong (either a false positive of false negative). Use a 0.05 significance level to test the claim that less than 10% of the test results are wrong. Does the test appear to be good for most purposes?

Testing a Claim about a Proportion In a survey of 703 randomly selected workers, 15.93% got their jobs through newspaper ads. Consider a hypothesis test that uses a 0.05 significance level to test the claim that less than 20% of workers get their jobs through newspaper ads.

Testing a Claim about a Proportion