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Exam2. A learning experience…. 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…. Question by Question. Data for Q1 to Q3. Numerical. Categorical. Numerical. Categorical. n=60. Q1.

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exam2

Exam2

A learning experience….

scores
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…
data for q1 to q3
Data for Q1 to Q3

Numerical

Categorical

Numerical

Categorical

n=60

slide5
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
slide6
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
q3 fuel type and mpg
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

q4a aspirin and heart attack
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)
q4b how many heart attacks using new design given ps
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

q4c will new design affect p value
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

q5 is di significantly better than el
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

q6 rportfolio
Q6. Rportfolio

R1, R2, R3

Will not be

Independent.

  • Rportfolio = (R1+R2+R3)/3

Sum of variances (independent)

.414/3

q7 total avg weight of n 20
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

q8 al and bo
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.
slide15
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…