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Here’s a summary of what we know and are about to learn…

Here’s a summary of what we know and are about to learn…. Those last two in read are the topic for today. Is there a difference?. Testing for the difference in population means – Chapter 24. Are athletes given a break in college admissions?.

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Here’s a summary of what we know and are about to learn…

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  1. Here’s a summary of what we know and are about to learn… Those last two in read are the topic for today.

  2. Is there a difference? Testing for the difference in population means – Chapter 24

  3. Are athletes given a break in college admissions? • A total of 23 Gossett High School students were admitted to the State University. Of those students, 7 were offered athletic scholarships. • The school’s guidance counselor looked at their composite ACT scores (shown next slide), wondering if State U. might admit people with lower ACT scores IF they were also athletes.

  4. The question • Do athletes admitted to State University have lower ACT scores?

  5. The data Composite ACT Scores Non-athletes Athletes • Let’s assume that these students are representative of students throughout the state.

  6. H-P-M-CHelping People Move Cows • Hypotheses: H0: The mean for non-athletes is the same for athletes. Ha: The mean for non-athletes is more than for athletes.

  7. H-P-M-CHappy Pandas Model Clothes • Plan: We are assuming that this group is representative of the state university population (or is the equivalent of a random sample.) The scores for each group are independent of each other. One sample does not depend on the other. Histograms or boxplots show that each sample is roughly symmetric and unimodal, i.e. plausibly normal The population is more than 10 times larger than the sample size (10% rule). With these conditions met, we can use a two sample t-test.

  8. A note on degrees of freedom in a two sample t-test You have two choices when doing a two sample t – test: • Take the smaller of the two samples and subtract one from the sample size. If the two samples are size 20 and 7, use 6 degrees of freedom and go to Table B. • Use the calculator’s computation of degrees of freedom (called Satterthwaite’s Formula). Both methods are acceptable.

  9. H-P-M-CHolding Poodles More Cheerfully • Mechanics: The average ACT for athletes is 21.86 while the average for non-athletes is 24.75. The bare details are that t = 2.02 with 10.13 degrees of freedom from the calculator. The p-value is then 0.035.

  10. H-P-M-CHorrible Penguins Maul Clown • Conclusion: With a p-value of 0.035 (less than 0.05), we reject the null hypothesis. There is strong evidence that average ACT scores for athletes are lower than for non-athletes.

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