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Lecture Slides

Lecture Slides. Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola. Chapter 8 Hypothesis Testing. 8-1 Review and Preview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim about a Proportion 8-4 Testing a Claim About a Mean: Known

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Lecture Slides

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  1. Lecture Slides Elementary StatisticsEleventh Edition and the Triola Statistics Series by Mario F. Triola

  2. Chapter 8Hypothesis Testing 8-1 Review and Preview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim about a Proportion 8-4 Testing a Claim About a Mean: Known 8-5 Testing a Claim About a Mean: NotKnown 8-6 Testing a Claim About a Standard Deviation or Variance

  3. Section 8-3 Testing a Claim About a Proportion

  4. Key Concept This section presents complete procedures for testing a hypothesis (or claim) made about a population proportion. This section uses the components introduced in the previous section for the P-value method, the traditional method or the use of confidence intervals.

  5. Part 1: Basic Methods of Testing Claims about a Population Proportion p

  6. Notation = population proportion (used in the null hypothesis) = number of trials (sample proportion)

  7. 1) The sample observations are a simple random sample. 2) The conditions for a binomial distribution are satisfied. 3) The conditions and are both satisfied, so the binomial distribution of sample proportions can be approximated by a normal distribution with and. Note: is the assumed proportion not the sample proportion. Requirements for Testing Claims About a Population Proportion

  8. Test Statistic for Testing a Claim About a Proportion Use the standard normal distribution (Table A-2) and refer to Figure 8-5 Use the standard normal distribution (Table A-2). P-values: Critical Values:

  9. Caution Don’t confuse a P-value with a proportion p. P-value = probability of getting a test statistic at least as extreme as the one representing sample data p = population proportion

  10. P-Value Method: Use the same method as described in Section 8-2 and in Figure 8-8. Use the standard normal distribution (Table A-2).

  11. Traditional Method Use the same method as described in Section 8-2 and in Figure 8-9.

  12. Example: A recent study showed that 53% of college applications were submitted online (based on data from the National Association of College Admissions Counseling). Assume that this result is based on a simple random sample of 1000 college applications, with 530 submitted online. Use a 0.01 significance level to test the claim that among all college applications the percentage submitted online is equal to 50%

  13. Example: • What is the test statistic? • What are the critical values? • What is the P-Value? • What is the conclusion? (Figure 8-7 on page 403) • Can a hypothesis test be used to “prove” that the percentage of college applications submitted online is equal to 50%, as claimed?

  14. Voting for the Winner • In a presidential election, 308 out of 611 voters said that they voted for the candidate who won (based on data from ICR Survey Research Group). 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?

  15. (determining the sample proportion of households with cable TV) Obtaining sometimes is given directly “10% of the observed sports cars are red” is expressed as sometimes must be calculated “96 surveyed households have cable TV and 54 do not” is calculated using

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