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=p_{0}

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).

H_{0} =.20 ,H_{a} ≠.20

p_{0}=.20 ,p=.15,n=100

Z_{calc}=(0.15-0.20)/(sqrt((.20*.80)/100))=-1.25

Z_{critical}=-1.96

Zcal is less than Z_{critical }, 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).

H_{0}>=.20 ,H_{a} <.20

p_{0}=.20 ,p=.15,n=100

Z_{calc}=(0.15-0.20)/(sqrt((.20*.80)/100))=-1.25

Z_{critical}=-1.645

Zcal is less than Z_{critical }, means failed to reject the null hypothesis again.

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