Question

Imagine a professor wants to examine if there is a relationship between gender and performance on a writing test. Thirty girls and thirty boys participated in his experiment. They were given a standard writing test and their grades were given as "outstanding", "good", "passing", and "failing". If the professor decided to use a Chi-square test to examine the relationship, how many degrees of freedom are there in this Chi-square test?When using the Chi-square test, the probability of Type I error is____ its significance level.a. Not related to b. Bigger thanc. Equal tod. Smaller than

Answer 1

Explanation:

Hello!

You have two populations "boys" and "girls" from each population a sample of 30 students is taken (n₁=n₂=30) and they resolved a standard writing test. After the test the categorized variable X: "grade obtained in a writing test" (CAT: Outstanding, Good, Passing and Failing" was registered.

The objective of the test is to determine if the variable has similar distribution across the different populations.

The statistic to use is:

χ²= ∑
`(O_(rc) - E_(rc) )/(E_(rc) )` ~ χ²
`_((r-1)(c-1))`

Where

r: number of populations

c: number of categories defined for the variable

In this case

χ²
`_((2-1)(4-1))` ⇒ χ²
`_(3)`

The probability of commiting a Type I error is for every hypothesis test, regarding the statistic or distribution applied, equal to the level of significance. Always.

I hope it helps!