Question

What z- score corresponds to one sided p- value of $0.95$ ?

Answer 1

Hint: To solve this question we need to know the concept of P value of one sided P value for the Z test. The p-value is a base is basically a probability with a value ranging from 0 to 1. One- sided tail value is used for the asymmetric distribution.

Complete step by step solution:
The question asks us to find z- score for one sided p-value for $0.95$. Z-score basically measures the relative position as for the certain value probability given. A standard normal table, also called the unit normal table. It is a mathematical table for the values of z, which represents the values of the cumulative distribution function of the normal distribution. Below is the Standard Normal Table for some values of z which are needed:

z	.04	.05	.06	.07	.08
0.7	0.2296	0.2266	0.1711	0.2206	0.2177
0.8	0.2005	0.1977	0.1949	0.1922	0.1894
0.9	0.1736	0.1711	0.1685	0.1660	0.1635
1.0	0.1492	0.1469	0.1446	0.1423	0.1401
1.1	0.1271	0.1251	0.1230	0.1210	0.1190

Using the above Standard Normal table, find the area in the right tail that is equal. The p-value $0.95$ will be found as the common of $0.9$ and $0.05$ is $0.1711$ . Now since the value of the difference is less than equal $0.5$ so the formula used to calculate the z- score will be:
$\Rightarrow 2\left( 1-value \right)$
$\Rightarrow 2\left( 1-0.1771 \right)$
$\Rightarrow 2\left( 0.8826 \right)$
$\Rightarrow 1.645$
$\Rightarrow z=1.645$
$\therefore $ The z- score corresponds to one sided p- value of $0.95$ is $1.645$ .

Note: There are two types of tailed tests: one is one tailed test while the other is two tailed tests. This question was on one tailed test. So refer to the question properly. The above formula is used because the value z is less than 2. It is used in null-hypothesis testing and testing for statistical significance.