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Exam 2 Learning Experience - Scores & Statistical Analysis

This text provides an overview of the learning experience during Exam 2, including the improvement in scores and the statistical analysis conducted on various questions.

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Exam 2 Learning Experience - Scores & Statistical Analysis

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  1. Exam2 A learning experience….

  2. Scores • Raw Scores went from 68 to 147 • As percentage of total….40% to 86% • Scaled scores went from 60.5 to 100 • Some still left to be graded…

  3. Question by Question

  4. Data for Q1 to Q3 Numerical Categorical Numerical Categorical n=60

  5. Q1 • expect that the size of the car engine (measured by displacement) would change based on car class (compact, midsize, large) • H0: MU(compact)=MU(mid)=MU(large) • Ha: not all equal • ANOVA single factor (3 samples) • Unstack the data, excel data analysis

  6. Q2 • expect to see a relationship between car class and recommended fuel type • Relationship between two categorical variables (car class and fuel type) • Chi-sq independence test • 3x2 contingency table of counts…summing to 60

  7. Q3. Fuel type and mpg • expect that because premium gasoline is higher quality, cars for which it is recommended will get higher gas mileage (on average) than cars for which regular fuel is recommended • Ho: MU(prem) = MU(reg) • Ha: MU(prem) > MU(reg) • Unstack, T-test two sample • NOTE: We guessed the wrong tail. • Do not reject HO in favor of THIS Ha. R got higher sample mean The wrong p value The correct p value

  8. Q4a Aspirin and Heart Attack • Relationship between two 0/1 variable. • 2x2 contingency table from the facts in the question (like lights and myopia). • Chi-sq independence test for 2T alternative. • Half the pvalue if you want a 1T alternative (Paspirin < Pplacebo)

  9. Q4b. How many heart attacks using new design (given Ps) • It is easy to calculate the mean (most likely) of 250.5. • Tell me that the actual number is a random variable • Provide a probability distribution for that random variable Normal approx to binomial

  10. Q4c. Will new design affect p-value? • Yes. We will be more certain about Aspirin’s effect and LESS certain about Placebo’s effect. • The test is focused on the difference. • The gain in accuracy for aspirin is not as great as the loss in accuracy for placebo (diminishing returns) • Our test will be less powerful. • P-value will go up. • 50/50 v 75/25 v 100/0 Best design Worst design

  11. Q5. Is Di significantly better than El? • Not about whether P=0.5 • About whether P(di)=P(el) • 2x2 chi-squared independence test 2 tailed p-value 1 tailed p-value

  12. Q6. Rportfolio R1, R2, R3 Will not be Independent. • Rportfolio = (R1+R2+R3)/3 Sum of variances (independent) .414/3

  13. Q7. Total (Avg) weight of n=20 • Mean = 20*μ • Variance = 20*σ2 • Normal (sum of normals) Family hotel means….. Weights in elevator not independent. More likely to be under 3500. Pr(total<3500) = NORMDIST(3500,3000,178.9,true) = 0.9974

  14. Q8. Al and Bo • Neither knows σ • Both get the same • Al uses t.dist, Bo uses normdist • The t correctly reflects extra uncertainty…giving Al a higher p-value • Bo’s cheating is rewarded with a lower p-value.

  15. Q9 • If students don’t cheat, then their IQs are independent identically distributed N(100,15) • The null hypothesis (mean men = mean women) IS TRUE!!! • When H0 is true, and we do any test correctly, we reject with probability 0.05. • We will reject H0 with probability 0.05 and fail to reject with probability 0.95 • What will happen under H0 is “easy” • What will happen under Ha is very difficult…

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