Earlier we discussed about the Hypothesis Testing , what is one sample and two sample tests. Also we have gone through one sample t and z test.
Here we are going to discuss p value and one sample p test.
What is p value ?
- p value is the lowest value of alpha for which the null hypothesis can be rejected.
- If p is lesser than alpha(usually it is .05), “reject the null hypothesis”.
- If p is higher than the alpha, “failed to reject the null hypothesis”.
Let’s say p=.001,null hypothesis is rejected.
Hope we are clear about the p value. Now let’s talk about one sample p test.
One Sample p test :
We calculate the z statistics only for the test.
Null Hypothesis: p=p0
Below is the formula to calculate the z statistics when percentage or proportion are given.

Let’s understand the test by solving one of the problem.
Problem – There is a town name ABC , where smoking rate as per the past data is 20% . Currently there are 100 samples are picked from the town and found 15 as smoker. Has the smoking rate changed?(95% confidence interval).
H0 =.20 ,Ha ≠.20
p0=.20 ,p=.15,n=100
Zcalc=(0.15-0.20)/(sqrt((.20*.80)/100))=-1.25
Zcritical=-1.96
Zcal is less than Zcritical , means failed to reject the null hypothesis. It means smoking rate is as same as past smoking rate 20%.
Let’s solve one problem related to smoking rate only.
Problem – There is a town name ABC , where smoking rate as per the past data is 20% Currently there are 100 samples are picked from the town and found 15 as smoker. Has the smoking rate reduced?(95% confidence interval).
H0>=.20 ,Ha <.20
p0=.20 ,p=.15,n=100
Zcalc=(0.15-0.20)/(sqrt((.20*.80)/100))=-1.25
Zcritical=-1.645
Zcal is less than Zcritical , means failed to reject the null hypothesis again.
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