Review

first question is a test of independence,

• when given that the student pop is 60% female; 7/100 were male and were wearing attire (is this probability of A and B or A given B? this is A and B); when 1 in 10 female student were wearing attire (Pr[CSU I F], in other words, A given B)

• if 60% are female then 40% are male; if 10% of females wear CSu then 90% dont; if 7% of men dont then the propability of 0.07/.4 = .175 and 1 - .175 = 0.825 is the prob that men dont

• remember that Pr M and CSU = PrM x P[CSU I M] → /07 = .4 x P[CSU I M] for findng .175

• now multiply the probability of male or female divided by the probabilities to find the given outcoms

• then add the propability of female and attire with male and attire and we find that .06 doesnt equal .078, therefore not independent

• or use a table

  • check out slides, i like this wayyyy better

Binomial Probability: n trials; p probability of successes

• X = 20; n = 20; p = 0.5

• 20! / 18!(2!) = 190

• then continue with the other formula

Hypothesis testing

• recognize the definition given on the slide, its asking for the p value

• understand how these questions are written

• Errors

  • If null is true and we reject → Type I

  • If null is false and we reject → Correct

  • If null is true and we fail to reject → Correct

  • If null is false and we fail to reject → Type II

  • remember that making our critical value too small will increase the Type II error

  • no what effect error rates

    • the differneces in means can determine the overlap of the distributions (Type II)

    • as difference in means goes up Type II goes down, as smaple size increases, Type II error decreases as well, leading to more reliable results in our hypothesis testing. As variance decreases Type II also decreases

Conditional Probabilites and Pr[A and B] vs Pr[A I B]

Interquartile range

• the boxes in a box and whisker plot tells us the concentration in variation of the 1st and 3rd quartiles, the solid line is the mean

Question about pea pods

• mutuall exclusive if the prob of A and B occuring together is 0, so to be short and yellow is not mutuall exclusive

• are yellow and short independent?

  • Pr[yellow] = .25

  • Pr[short] = .25

  • .25 x .25 × 1600= 100

  • so yes independent bc observed matches expected

identify types of data

• blood type - categorical and nominal

• age - numerical (discrete [nearest integer value])

• Pain Level (1-5 scale) - categorical and ordinal (theres a specific order)

• Temperature - Numerical (continuous [nearest decimal place])

• weight - numerical (continuous)

• number or partners - numerical discrete

• Energy level (low, medium high) - categorical ordinal