Class 13The IQ Experiment

9.39.4

10.210.410.58.18.3

H0:

Ha:

Test Statistic

Calculation of p-value

9.3

H0:

Ha:

Test Statistic

Calculation of p-value

9.3

𝒁 σ

s is the sample standard

deviation.Calculated using

=stdev()

Using s in place of σ, changes the

Z-statistic to a t-statistic.

H0: μ=100

Ha: μ>100

Calculation of p-value

= T.DIST.RT(calculated t, dof)=

9.4

n-1

H0: μM = μF

Ha: μM ≠ μF

Test Statistic(use Excel

DataAnalysis, t-test 2-sample = variances)

Calculation of p-valueExcel will give it to you…. or=t.test(array1,array2,2,2)=

2 tails 2 sample

10.2If you have the data….

H0: μM = μF

Ha: μM ≠ μF

Calculation of p-value=t.dist.2t(calculated t,dof) =

Test Statistic

10.2

n1+n2-2

If you only have the summary statistics….

Page 415

Class 14 will be about Paired Tests

H0: μfall = μspring= μother

Ha: they are not =

Test Statistic

F-statistic

Calculation of p-value

Use DataAnalysis, ANOVA: single factor

10.4 and 10.5 applied

Confidence Intervals8.1 and 8.3

If you know μ and σ

95% probability interval for

𝜇∓1.96× 𝜎√𝑛

If you know and σ

95% confidence interval for

𝑋𝑛∓1.96×𝜎√𝑛

If you know and s

95% confidence interval for

𝑋𝑛∓𝑡 .𝑖𝑛𝑣 .2 𝑡(0.05 ,𝑑𝑜𝑓 )× 𝑠√𝑛

There is a 95% pwill fall in this interval

There is a 95% pthis interval will cover μ.

There is a 95% pthis interval will cover μ.

8.1 and 8.3

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.