8.4 Testing a claim about a Mean (σ known)
8.4 Testing a claim about a Mean (σ known)
What we know
̅
𝒙
Sample mean
𝒏
Sample size
𝝈
Population standard deviation
𝝁𝟎
Assumed mean
𝜶
Significance level
Example
Use a 0.1 significance level to test the claim that a population
mean is greater than 166.3 given a sample of size 40 whose
mean is 172.55 and the population standard deviation is known
to be 26
H0 : μ = 166.3
H1 : μ > 166.3
Stat → Z statistics → One sample → With summary
Sample mean 𝟏𝟕𝟐. 𝟓𝟓
Standard deviation
Sample size
𝟐𝟔
𝟒𝟎
● Hypothesis Test
Null: mean=
Alternative
𝟏𝟔𝟔. 𝟑
>
P-value = 0.0642
Since P-Value < α, reject H0 (initial), accept the claim (final)
8.4 Testing a claim about a Mean (σ known)
Step 1
Stat → Z statistics → One sample → With summary
On the StatCrunch window select:
Stat, Z statistics, One sample, with summary
Step 2
Sample mean
Standard deviation
Sample size
̅
𝒙
𝝈
𝒏
̅ in ‘Sample mean’
Enter 𝒙
Enter 𝝈 in ‘Standard deviation’
Enter 𝒏 in ‘Sample size’
Click ‘Next’
Step 3
● Hypothesis Test
Null: mean=
Alternative
𝝁𝟎
#
Select ‘Hypothesis Test’
Enter ‘Null: mean=’ with 𝝁𝟎
Select sign used in H1 in ‘Alternative’
Click ‘Calculate’
Step 4
Read the P-value from ‘P-value’
P-value
Read the Test statistic from ‘Z-Stat’
Test statistic