How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 9
b. 7
c. 62
d. 74

a. 9

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".  

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".  

We assume that we have the following system of hypothesis:

H0: The data follows the distribution proposed

H1: The data not follows the distribution proposed

The statistic to check the hypothesis is given by:  

This statistic have a Chi Square distribution distribution with k-1 degrees of freedom, where n represent the number of categories on this case k=10. And if we find the degrees of freedom we got:

a. 9

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.