Arandom sample of 100 high school students was surveyed regarding their favorite subject. the following counts were obtained: favorite subject number of students english math science 30 art/music the researcher conducted a test to determine whether the proportion of students was equal for all four subjects. what is the value of the test statistic? o b. 25 d. -4 how many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories? a. 74 d. 62

a)

b)

Step-by-step explanation:

We assume the following info:

Favorite Subject         Number of students

English                                    25

Math                                        30

Science                                   30

Art/Music                                 15

Total                                        100

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".

Part a

The system of hypothesis on this case are:

H0: There is no difference with the distribution proposed

H1: There is a difference with the distribution proposed

The level os significance assumed for this case is

The statistic to check the hypothesis is given by:

The table given represent the observed values, we just need to calculate the expected values are 25 for each category.

And the calculations are given by:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom for the statistic given by:

And we can calculate the p value given by:

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(6,3,TRUE)"

Part b

For this case we have this formula:

what are the statments

step-by-step explanation: