## Description

1. There are 3 chi-square tests - The goodness of fit test, the test of independence, and the test for homogeneity. What's the difference among the three? Why would you use one over another?

2. There are one-sampled and two-sampled t-tests and BOTH can be either one-tailed or two-tailed. When is a t-test one-tailed? When is it two-tailed? Can you give me examples for both?

## Explanation & Answer

Here is your assignment with plagiarism result )

1

QUESTION 1:

There are 3 chi-square tests - The goodness of fit test, the test of independence, and the test for

homogeneity. What's the difference among the three? Why would you use one over another?

Answer

Difference of goodness of fit test, the test of independence, and the test for homogeneity

In goodness of fit test, we compare observed value of one variable with assumed

distribution while in the independence test, we test whether two variables are independent or not.

The independence tests and the homogeneity tests were obtained the same for categorical

variables and the test procedures, but they differ in finding expected frequencies. Among these

three chi-square tests, I would use the homogeneity test. This is because, as we use this test, we

can evaluate if the variances are equal. Also, we know assumptions for independent samples ttest which states that population variances should be approximately equal and if this assumption

of homogeneity of variance is violated, then finding the pooled variance for this test cannot be

meaningful because of comparative difference between the population variances increases.

2

QUESTION 2:

There are one-sampled and two-sampled t-tests and BOTH can be either one-tailed or twotailed. When is a t-test one-tailed? When is it two-tailed? Can you give me examples for both?

Answer

When it comes to one-tailed test, the statistical hypothesis test in which alternative hypothesis

has only one end. Determines if there is a relationship between variables in single direction

For example:

A carpenter wishes to claim that his power of fan last longer than 12 hours. A random sample of

power of fan is 8 and has mean power of 9 hours and a standard deviation of 2 hours. Set up fan

finding hypothesis tests at 5% level...

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