SM339

1
SM339

• SM339 will continue where SM239 left off
• Where did SM239 leave off?
• SM239 dealt with the measurement of random
  processes
• Deductive given the process, determine
  characteristics
• Inductive given the characteristics (data),
  determine parameters of the process

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SM339

• Processes
• Binomial
• Poisson
• Neg bin, Erlang (waiting time)
• Hypergeometric (?)
• Normal, t

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SM339

• Confidence bounds/ intervals
• Based on what would be unusual
• Suppose we observe 7 successes in 10 trials of a
  binomial process
• Find a 90 upper bound for p
• For an upper bound, it would be unusual to have
  so few successes
• Solve 0.10 Prob(0-7 succ for given p)

4
SM339

• BRPOB(N, p, lo, hi) returns probability from LO
  to HI (inclusive)
• BISECT(fn, value, lo, hi, tol)
• Finds where fn(x)value, given that the answer is
  between LO and HI
• NOTE if the result is very close to LO or HI,
  this suggests that LO or HI are wrong. Change LO
  and/or HI and try again.
• Result is to within TOL
• Bisect(_at_(p) BPROB(10,p,0,7), 0.10, 0.01, 0.99,
  0.0001)
• Ans0.8842

5
SM339

• Poisson PPROB(T, rate, lo, hi)
• Ngbprob(R, p, lo, hi)
• Erlangprob(R, rate, lo, hi)
• NPROB(mu, sd, lo, hi)
• TPROB(mu, sd, df, lo, hi)
• For unbounded RV (Poisson, erlang, normal), use
  large values for HI or small values for LO
• For normal, go 4-5 SD away from the mean

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SM339

• Exercises
• 1. Given 4 successes in 11 trials, find 95 lower
  bound for p
• 2. Given 3 events in 2.5 hrs (Poisson), find 95
  upper/ lower bound for rate
• 3. If SD5.5 and avg of 6 obs is 12.2, find 90
  conf interval for the mean

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SM339

• Order statistics
• Suppose we have a sample of size 8 from a normal
  distribution with SD3.1
• The 3rd largest obs is 24.6
• Find 90 lower bound for the mean

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SM339

• For a lower bound, it would be unusual for the
  observation to be so high
• 0.10 Prob(3rd largest 24.6)
• Prob(at least 3 obs 24.6)
• bprob(8, nprob(m,3.1,24.6,99), 3, 8)
• Ans21.3449

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SM339

• When N is odd, the sample median is an order
  statistic
• N9, 5th largest (smallest) is the sample median
• So instead of using the average for confidence
  bounds, we can use the sample median

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SM339

• Outline for SM339
• 1. Hypothesis Testing
• 2. Extend 2 sample cases to 2 samples
• Compare several probabilities
• Compare several means (ANOVA)

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SM339

• 3. Fitting a line to data regression
• 4. Fitting a linear fn of several variables
  multiple regression
• 5. Applications of multiple regression after
  Spring Break
• 6. Principal Components when data are vectors
  rather than scalars
• 7. Logistic Regression binary response