Question

1. Explain the difference between non-directional and directional hypotheses, and explain in which circumstances it is important to apply directional hypothesis.
2. Explain why Chi square distributions are positively skewed and what is its relationship with the degrees of freedom.
3. The objective of hypothesis testing is to reject the null hypothesis. How do we use the P-value to accomplish this goal?
4. Describe the difference between One-way versus Two-way ANOVA and provide an example of each.

Answer 1

difference between non directional and directional hypothesis are as follows:

directional hypothesis	non -directional hypothesis
Directional hypothesis are those where one can predict the direction.effect of one variable on other as positive or negative	non directional hypothesis are those where one cannot predict the kind of effect but can state a relationship between variable 1 and variable 2.

chi square distribution is always positive below are the given reasons about why it is always positively skewed:

The computed value of Chi-Square is always positive because the difference between the Observed frequency and the Expected frequency is squared, that is ( O - E )² and the denominator is the number expected which must also be positive.

There is a family of Chi-Square distributions. There is a Chi-Square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on.

The shape of the Chi-Square distribution does not depend on the size of the sample. It does depend upon the number of categories.

The Chi-Square distribution is positively skewed. However, as the number of degrees of freedom increases, the distribution begins to approximate the normal distribution.