MTH 174 – Statistics I
Formula Sheet—for Chapters 8 & 9
Confidence Intervals
Critical Values of 𝑧
Confidence Level (𝒄)
𝜶=𝟏−𝒄
𝒛𝜶/𝟐
0.80
0.20
1.28
0.85
0.15
1.44
0.90
0.10
1.645
0.95
0.05
1.96
0.98
0.02
2.33
0.99
0.01
2.575
Margin of Error of a Confidence Interval for a
Population Proportion
𝐸=𝑧𝛼/2⋅√𝑝̂(1−𝑝̂)
Critical values for estimating a population variance or
standard deviation
For a confidence level of 𝑐, where 𝛼=1−𝑐, and
𝑛−1 degrees of freedom:
Confidence interval for estimating a population
variance (𝑛−1)𝑠2
𝜒𝛼/2
2<𝜎2<(𝑛−1)𝑠2
𝜒(1−𝛼/2)
2
Confidence interval for estimating a population
standard deviation
√(𝑛−1)𝑠2
𝜒𝛼/2
2<𝜎<√(𝑛−1)𝑠2
𝜒(1−𝛼/2)
2
Confidence Intervals for Two Samples
Margin of Error of a Confidence Interval for the
Difference between Two Population Means
(𝜎 Unknown, Unequal Variances)