STAT100: Statistics Midterm 2

finite vs infinite quantities, e.g. tails observed in 100 coin flip vs. possible test scores

normal symmetric distribution model in which the mean is 0 and SD is 1

distribution for all possible values from a sample n

regardless of distribution shape, the sample mean distribution becomes more normal as n increases. generally comparable to population if n > 30

population: μ, σ, p
sample: x̄, s, p^

1 SD: 68% (34%)
2 SD: 95% (13.5%)
3 SD: 99.7% (2.35%)
outside edge: .15%

p hat is for qualitative variables and x bar is quantitative

proportions (qualitative, p hat) and means (quantitative, x bar)

90% - 1.645
95% - 1.96
99% - 2.575
critical value x square root (p(1-p)/n) = margin for error, E

n>30 for a known population SD, n>75 for unknown. if not, t critical values must be used
critical value x (standard deviation/square root (n))

null: H0, no change
alt.: H1, change

either reject the null or fail to reject the null

random sampling + np(1-p) > 10

p unequal to p - two tailed
p < p - left tailed
p > p - right tailed

(p hat - p)/ square root of ((p(p-1))/n)