Study Guides
(234,551)

United States
(117,842)

Statistics
(13)

STAT 301
(11)

Brett Hunter
(9)

Midterm

#
Hypothesis tests for μ, p-values for t-tests
Hypothesis tests for μ, p-values for t-tests

Hypothesis tests for μ, p-values for t-tests

Unlock Document

Colorado State University

Statistics

STAT 301

Brett Hunter

Fall

Description

7 October
Hypothesis Tests for μ
2 cases
σ known – rarely happens
σ unknown
σ known
Test statistic
x−μ
0
σ
Z test ~ N(0,1)
√n
Assuming that n ≥ 30 (or X has a normal distribution i.e., normal population
distribution)
p-value
If HA: μ > μ0, then p-value = P(Z > Z )test
If HA: μ < μ0, then p-value = P(Z < Z )test
≠
If HA: μ μ0, then p-value = P(Z > |Z |test
σ unknown
Assumption is still n ≥ 30 (or X~Normal)
Test statistic
x−μ
0
s
ttest ~ tn-1
√n
Follows t-distribution with n – 1 degrees of freedom
p-value
If HA: μ > μ0, then p-value = P(t n-1> ttest
If HA: μ < μ0, then p-value = P(t n-1 )test ≠
If HA: μ μ 0 then p-value = 2 P(t n-1 > |test
How to find P(t > t )?test
Use Table 4
Recall that the t-distribution is symmetric and based on some degrees of freedom
Using Table 4
Table gives probabilities where P(t > t ) can

More
Less
Related notes for STAT 301