Hypothesis Testing with TWO Samples

Section 8.1

2 samples are independent if the sample selected from one population is not related to the sample selected from the 2 nd 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)

6. 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. 8. Sample 1: the IQ scores of 60 females Sample 2: The IQ scores of 60 males

3 ways the NULL hypothesis can be written: µ 1 = µ 2 µ 1 µ 2 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.

1. State the hypotheses 2. Specify level of significance, α 3. Determine the critical value(s) 4. Shade the rejection region(s) 5. Find the test statistic, z (new formula) 6. Make decision to reject or not reject H 0 7. Interpret the decision in context

 18. Claim: µ 1 ≠ µ 2 α = 0.05 Sample statistics: mean 1 = 52, s 1 = 2.5, n 1 = 70 mean 2 = 45, s 2 = 5.5, n 2 = 60

 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 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 is $1878 and the standard deviation is $85. At α = 0.05, can you support the restaurant association’s claim?

Section 8.2

 10. Claim: µ 1 < µ 2 α = 0.10 Sample statistics: Mean 1 = 0.345, s 1 = 0.305, n 1 = 11 Mean 2 = 0.515, s 2 = 0.215, n 2 = 9 Assume σ 2 1 = σ 2 2  12. Claim: µ 1 > µ 2 α = 0.01 Sample statistics: Mean 1 = 52, s 1 = 4.8, n 1 = 16 Mean 2 = 50, s 2 = 1.2, n 2 = 14 Assume σ 2 1 ≠ σ 2 2

 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. AthletesNON Athletes Mean 1 = 56 ml/kg/minMean 2 = 47 ml/kg/min s 1 = 4.9 ml/kg/mins 2 = 3.1 ml/kg/min n 1 = 23n 2 = 21