Hypothesis Testing for Proportion

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Presentation transcript:

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. The sample observations are a simple random sample. The conditions for a binomial sample are satisfied. The conditions 𝑛𝑝≥5 and 𝑛𝑞≥5 are both satisfied. Test Statistic for Testing a Claim about a Proportion 𝑧= 𝑝 −𝑝 𝑝𝑞 𝑛

Testing a Claim about a Proportion P-value method in 5 Steps State the hypothesis and state the claim. Compute the test value. (Involves find the sample statistic). Draw a picture and find the P-value. Make the decision to reject 𝐻 0 or not. (compare P-value and 𝛼) 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. 𝐻 0 :𝑝=.8 and 𝐻 1 :𝑝>.8(claim) Note: 𝑝 = 1864 2246 =.83 𝑧= 𝑝 −𝑝 𝑝𝑞/ 𝑛 = .83−.8 .8 (.2)/ 𝑛 =3.544 P-value is 0.000196 or 0 Since 0 <0.05(significance level) reject the null. There is sufficient evidence to support the claim that 80% of adults believe that texting should be illegal. Or use [stat]→Test →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