Question

How do you find the p-value of a two tailed test when $z=1.97 ?$

Answer 1

To solve this question we need to know the concept of statistics. To be more precise the question is of topic One- sample Hypothesis Test for p. We need to refer to the Standard Normal Distribution table for finding the value of p. We expand the value of $z$ in terms of two in such a way that one term is in row and other in column.

Complete step-by-step solution:
The question asks us to find the p-value of a two tailed test when $z=1.97$. A p-value is a measure of the probability that an observed difference could have occurred just by random chance. A two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. To solve this we will refer to the normal curve table.
The below table entries represent the area under the standard normal curve from $0$ to the specified value of $z$.

z	.05	.06	.07	.08	.09
1.7	0.4599	0.4608	0.4616	0.4535	0.4633
1.8	0.4678	0.4686	0.4693	0.4625	0.4706
1.9	0.4744	0.4750	0.4756	0.4756	0.4767
2.0	0.4798	0.4803	0.4808	0.4812	0.4817
2.1	0.4846	0.4846	0.4850	0.4854	0.4857

The value of $z$ given in the question is $1.97$ . So we can write the number $1.97$ into $1.9$ and $0.07$ which mathematically would be written as $1.97=1.9+0.07$.
As we can see that the ${{1}^{st}}$ column and ${{1}^{st}}$ row are given in the table to give information about z value. All other cells contain P values.
We will come down along the ${{1}^{st}}$ column and locate $1.9$.
We will go along the ${{1}^{st}}$ row, located $0.07$.
We will move down vertically from $0.07$ and go horizontally from $1.9$. The meeting point of these two values gives the P value which is $0.4756$ as highlighted in the above image for the given $z$ value.
$\therefore$ The P value for $z=1.97$ is $0.4756$ .

Note: There are two types of tailed test one is one tailed test while other is two tailed test. This question was on two tailed tests. So refer to the question properly. It is used in null-hypothesis testing and testing for statistical significance. In the case of the two-tailed tests, we are testing a hypothesis that does not include a directional relationship.