Question 1156754
<font color=black size=3>
z = (phat - p)/(sqrt(p*(1-p)/n))
z = (0.841 - 0.8)/(sqrt(0.8*(1-0.8)/156))
z = 1.28022458967168
z = 1.28 is the test statistic
Nice job on getting the correct test statistic


Now use a Z table found in the back of your stats textbook to find the area under the standard normal distribution.  
If you do not have a book with you, then you can use a Z table such as this one
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
To find that
P(Z < 1.28) = 0.89973
note how I've highlighted the proper row and column which represent 1.20 and 0.08 combining to 1.28
<img src = "https://i.imgur.com/JZQtPB0.png">


So,
P(Z > 1.28) = 1-P(Z < 1.28)
P(Z > 1.28) = 1-0.89973
P(Z > 1.28) = 0.10027 approximately


Due to the "not equal" sign in the alternative hypothesis, we have a two tailed test. This means we will double the result to get the area in both tails. 


2*0.10027 = 0.20054


<font color=red size=4>The p value is approximately 0.20054</font>



Extra Info:
At the significance level alpha = 0.01, we fail to reject the null. We can only reject the null if the p value is smaller than alpha. Failing to reject the null means we effectively "accept" the null hypothesis (until other data comes along to invalidate it). In other words, we conclude that p = 0.8 is the case. In the context of the problem, we conclude that 80% of patients quit smoking after one month.
</font>