8.3 Testing a claim about a Proportion
8.3 Testing a claim about a Proportion
What we know
𝒙
Number of successes
𝒏
Number of observations
̂=
𝒑
𝒙
𝒏
Sample Proportion
𝒑𝟎
Claimed Proportion
𝜶
Significance Level
̂
Note: If the problem gives sample proportion 𝒑
̂
then find 𝒙 using:
𝒙=𝒏∙𝒑
Example
Use a 0.05 significance level to test the claim that a population
proportion is greater than 0.5 given a sample of size 14 with 13
H0 : p = 0.5
successes.
H1 : p > 0.5
Stat → Proportions → One sample → With summary
Number of Successes 𝟏𝟑
Number of observations 𝟏𝟒
● Hypothesis Test
Null: proportion= 𝟎. 𝟓
Alternative >
P-value = 0.0007
Since P-Value < α, reject H0 (initial), accept the claim (final)
8.3 Testing a claim about a Proportion
Step 1
Stat → Proportions → One sample → With summary
On the StatCrunch window select:
Stat, Proportions, One sample, with summary
Step 2
Number of Successes
Number of observations
𝒙
𝒏
Enter 𝒙 in ‘Number of successes’
Enter 𝒏 in ‘Number of observations’
Click ‘Next’
Step 3
● Hypothesis Test
Null: proportion=
Alternative
𝒑𝟎
#
Select ‘Hypothesis Test’
Enter ‘Null: prop.=’ with 𝒑𝟎
Select sign used in H1 in ‘Alternative’
Click ‘Calculate’
Step 4
Read the P-value from ‘P-value’
Read the Test statistic from ‘Z-Stat’
P-value
Test statistic