Let Z be a random variable following the standard normal distribution with mean µ = 0 and standard deviation σ = 1.
The 67th percentile of the distribution is the value z that separates the bottom 67% of the distribution from the top 100% - 67% = 33%. In terms of probability, we have
Pr[Z ≤ z] = 0.67
Use the inverse CDF for the normal distribution (or lookup z scores in a table) to find
z = ɸ⁻¹(0.67) ≈ 0.4399
where ɸ(z) is the CDF for the normal distribution.
There are a lot of ways to test for an hypothesis. There are known five steps of a test of hypothesis through the use of the critical value approach. They are;
- One has to Specify the Null Hypothesis.
- You have to also specify the Alternative Hypothesis.
- Then you set the Significance Level.
- Calculate the Test Statistic and Corresponding P-Value.
- Lastly, Draw a Conclusion.
<h3> The critical value approach?
</h3>
- This is known as a method that involves the determining of the "likelihood" or "unlikelihood" by knowing if or not the observed test statistic is said to be of a more extreme measure than would be expected if the null hypothesis were true.
It often uses the sample data and then there is an assumption if the null hypothesis is true before one can calculate the value of the test statistic.
Learn more about the critical value approach from
brainly.com/question/7472579
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