Question

1. Which Hypotheses Tests use a Chi-squared distribution?
2. Which Hypothesis Tests use an F distribution?
3. What is the rule for sample size calculations?
4. What is the rule regarding the appropriate signs to be used in the null and alternative hypotheses?

Answer 1

1. Chi squared distribution is generally used in hypothesis testing to test relationship between categorical variables.Null hypothesis states that there is no association between the categories or variables. Alternative hypothesis states that  there is an association between the two variables. This statistic is also called "goodness of fit" statistic,

2. F distribution is generally used in hypothesis testing, based on the calculated F statistic , to test if the variability is statistically significant. Here,the null hypothesis is  that the addition of the new factor does not cause a significant difference in variability.

3.Sample is a part of the population that helps us to draw inferences about the population.We need an appropriate sample size for that.Though, here is no certain rule of thumb to determine the sample size. We, can follow the following steps to get a better sample size .

a) Using a sample one calculates the population parameter. Thus, we should determine the confidence intervals, so that all the values of the sample lie within that interval range.

b)Larger sample is always better. So, one should try to take sample as large as possible.

c) A target for the power of a statistical test is to be applied when the samplee is collected.

4. As, the Null Hypothesis is always oppsite to the alternative hypothesis. We, can state the following mentioned rule regarding signs of hypothesis.