Problem 31

  1. Sample size is small, nearly normal model, probably representative enough

  2. 28.78 mean 0.4 is sd
  3. (28.78, 29.20)
  4. We are 95% confident that the true mean of weight of ruffles is between 28.3 and 29.2

  5. The company is going slightly below expectations to be safe

Problem 33

  1. Type 1
  2. yes, p value 0.02 is low enough to reject null

Problem 35

  1. Assuming a nearly normal model, that these samples were less than 10% of all chips ahoy, that the bags were chosen randoml (therefore independent), and that the sample size is big enough to be representative
  2. 1187.9,1288.4
  3. H0: chips=1000 Ha: chips>1000 p value = ~0 The company kept true to their word

Problem 37

  1. Plot, kept for one outlier, seems to be unimodal and symetric (nealy normal), and mets the conditions for probably representative as well, meaning we can procede to use the T model
  2. p value=0.015

THere is only a 1% chance that the true mean is 60 seconds while we observed the results in the smaple. This is too low to maintain our H0, so we reject that and assume that the true mean time is not 60 seconds.

  1. p value = ~0. We are more certain that the true mean of these rats time’s is not 60 seconds.
  2. No.

Problem 39

  1. (287.3, 289.9)
  2. not random, leading professionsal do not represent
  3. Yes, means not individual golfs