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 than
c. Equal to

b. Smaller than

If the probability value of a Chi square of 3.2 with a degree of freedom of 3 is 0.368, then we should___.
a. Fail to reject the null hypothesis       
b. We cannot decide unless we get the information on t-value
c. Reject the null hypothesis       
d. We cannot decide unless we get the information on factors and levels

Answer 1

1) how many degrees of freedom are there in this Chi-square test?

Answer:- we have two rows, one for girls and one for boys. Four columns, one for each “outstanding”, “good”, “passing”, and “failing”.

we know degree of freedom = (number of rows -1)*(number of columns -1)

we have number of rows =2 and number of rows = 4

so, we get

degree of freedom = (2 -1)*(4 -1) = 1*3 = 3

so, required degree of freedom = 3

2) When using the Chi-square test, the probability of Type I error is____ its significance level.
Answer:- we know that probability of type I error is always equal to the significance level. So, for chi square test, the probability of type I error is equal to its significance level.

So, answer is "equal"

3)If the probability value of a Chi square of 3.2 with a degree of freedom of 3 is 0.368, then we should___.

Answer:- At 0.05 or 0.10 level of significance, the result is insignificant because the p value is greater than significance level. So, we failed to reject the null hypothesis

So, option A is correct.