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CHAPTER EIGHT

Learn to test differences between means with large and small independent sample sets. Understand how to classify samples as dependent or independent, set hypotheses, determine significance levels, calculate critical values and test statistics, and make decisions based on outcomes. Practice analyzing scenarios like SAT score changes and spending habits among different age groups using appropriate statistical methods.

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CHAPTER EIGHT

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  1. CHAPTER EIGHT Hypothesis Testing with TWO Samples

  2. Section 8.1 Testing the difference between Means (large independent samples)

  3. Dependent/independent 2 samples are independent if the sample selected from one population is not related to the sample selected from the 2nd population. 2 samples are dependent if each member of one sample corresponds to a member of the other sample. (a.k.a. Paired or Matched samples)

  4. EX: classify as dependent or independent & explain • Sample 1: the SAT scores of 44 high school students. Sample 2: the SAT scores of the same 44 high school students after taking an SAT preparation course. • Sample 1: the IQ scores of 60 females Sample 2: The IQ scores of 60 males

  5. Changes from ch 7 3 ways the NULL hypothesis can be written: µ1 = µ2 µ1 < µ2 µ1> µ2 The samples must be randomly selected, independent, and each sample size must be at least 30 If n is not > 30, then each population must have a normal distribution with σ known.

  6. Guidelines… same as ch 7! • State the hypotheses • Specify level of significance, α • Determine the critical value(s) • Shade the rejection region(s) • Find the test statistic, z (new formula) • Make decision to reject or not reject H0 • Interpret the decision in context

  7. New formula for z

  8. 18. Claim: µ1 ≠ µ2α = 0.05 Sample statistics: mean1 = 52, s1 = 2.5, n1 = 70 mean2 = 45, s2 = 5.5, n2 = 60

  9. 28. A restaurant association says that households in the US headed by people under the age of 25 spend less on food away from home than do households headed by people ages 65-74. The mean amount spent by 30 households headed by people under the age of 25 is $1876 and the standard deviation is $113. The mean amount spent by 30 households headed by people ages 65-74 is $1878 and the standard deviation is $85. At α = 0.05, can you support the restaurant association’s claim?

  10. Section 8.2 tESTING the difference between means (small independent samples)

  11. Uses a t-test

  12. Test the claim • 10. Claim: µ1 < µ2 α = 0.10 Sample statistics: Mean1 = 0.345, s1 = 0.305, n1 = 11 Mean2 = 0.515, s2 = 0.215, n2 = 9 Assume σ21 = σ22 • 12. Claim: µ1 > µ2 α = 0.01 Sample statistics: Mean1 = 52, s1 = 4.8, n1 = 16 Mean2 = 50, s2 = 1.2, n2 = 14 Assume σ21 ≠ σ22

  13. 14. The maximal oxygen consumption is a way to measure the physical fitness of an individual. It is the amount of oxygen in milliliters a person uses per kilogram of body weight per minute. A medical research center claims that athletes have a greater mean maximal oxygen consumption than non-athletes. The results for samples of the 2 groups are shown below. At α = 0.05, can you support the center’s claim? Assume the population variances are equal.

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