Question

Determine if the statements below are true or false:

The chi-square distribution, just like the normal distribution, has two parameters, mean and standard deviation.

The chi-square distribution is always right skewed, regardless of the value of the degrees of freedom parameter.

The chi-square statistic is always positive.

As the degrees of freedom increases, the shape of the chi-square distribution becomes more skewed.

"If you found χ2 = 10 with df = 5, you would fail to reject the Null hypothesis at the 5% significance level".

Pt 2:

Consider a Chi-square distribution with degrees of freedom, df = 7. What is the I. mean; II. the standard deviation, for this distribution?

Consider a Chi-square distribution for a categorical variable with 4 levels. I. What is the degrees of freedom for this distribution? II. The chi-square test statistic was calculated to be 8.012. What is the p-value for this distribution?

Will give a thumbs up. Thank you for the help!!

Answer 1

The chi-square distribution, just like the normal distribution, has two parameters, mean and standard deviation. false

The chi-square distribution is always right skewed, regardless of the value of the degrees of freedom parameter. : true

The chi-square statistic is always positive. : false (as it can be 0 too)

As the degrees of freedom increases, the shape of the chi-square distribution becomes more skewed. false

"If you found χ2 = 10 with df = 5, you would fail to reject the Null hypothesis at the 5% significance level". True

Pt 2: mean =7

std deviation=sqrt(2*7)=3.74

Consider a Chi-square distribution for a categorical variable with 4 levels. I. What is the degrees of freedom for this distribution=3

II. The chi-square test statistic was calculated to be 8.012 ; p value= 0.0458