Transcript Class 11 - University of Virginia

Class 13
The IQ Experiment
9.3
9.4
10.2
10.4
10.5
8.1
8.3
9.3
H0:
Test Statistic
Ha:
Calculation of p-value
9.3
H0:
Test Statistic
Ha:
Calculation of p-value
σ
Using s in place of σ,
changes the
Z-statistic to a
t-statistic.
s is the sample
standard
deviation.
Calculated using
=stdev()
9.4
H0: μ=100
Test Statistic
Ha: μ>100
Calculation of p-value
= T.DIST.RT(calculated t, dof)
=
n-1
If you have the data….
10.2
Test Statistic
H0: μM = μF
(use Excel
DataAnalysis, t-test 2sample = variances)
Ha: μM ≠ μF
Calculation of p-value
Excel will give it to you….
or
=t.test(array1,array2,2,2)=
2 tails
2 sample
If you only have the summary statistics….
H0: μM = μF
10.2
Test Statistic
Page 415
Ha: μM ≠ μF
n1+n2-2
Calculation of p-value
=t.dist.2t(calculated t,dof) =
Class 14 will be about Paired
Tests
10.4 and 10.5
applied
H0: μ
fall
= μspring= μother
Ha: they are not =
Test Statistic
F-statistic
Calculation of p-value
Use DataAnalysis, ANOVA: single factor
Confidence Intervals
8.1 and 8.3
If you know μ and σ
95% probability interval for 𝑋𝑛
8.1 and 8.3
𝜎
𝜇 ∓ 1.96 ×
𝑛
If you know 𝑋𝑛 and σ
95% confidence interval for μ
𝜎
𝑋𝑛 ∓ 1.96 ×
𝑛
If you know 𝑋𝑛 and s
There is a 95%
probability 𝑋𝑛 will fall in
this interval
There is a 95%
probability this interval
will cover μ.
95% confidence interval for μ
𝑠
𝑋𝑛 ∓ 𝑡. 𝑖𝑛𝑣. 2𝑡(0.05, 𝑑𝑜𝑓) ×
𝑛
There is a 95%
probability this interval
will cover μ.
Today we learned….
• Three new hypothesis tests involving MEANS of
numerical random variables.
– All our earlier hypotheses tests were about categorical
random variables. (stacker, sales, admin) (success,
fail) (38 wheel segments) (Jan, Feb, … Dec)
– One-sample, two-sample, ANOVA-single factor
• What to do when we use s in place of σ.
– Switch from the normal/z to the t
• dof (n-1 or n1+n2-1) informs the t how good our estimate of
σ is.