Which is true about chi-square distributions?

A teacher has a theory that as students advance in grades, more students will have jobs. The teacher’s theory is that students having jobs will follow the ratio $1:2:2:3$ and that 12.5% of the 9th grade students have jobs. The teacher takes a sample of 100 students from each grade and finds the following number of students with jobs in each grade: 9th grade: 12, 10th grade: 22, 11th grade: 27, 12th grade: 35.

Calculate $x^2_c$ for the sample.

A high school principal surveyed students in grades 9–12 about their satisfaction with school lunches. The results are below:

What is the expected count for the cell corresponding to 9th graders not satisfied with school lunch?

What is an appropriate null and alternative hypotheses for a chi-square test for independence?

Which of these is NOT a condition for making statistical inferences when testing a chi-square distribution for independence or homogeneity?

What is the p-value for a chi-square test for independence or homogeneity if the number of rows is 4 and the number of columns is 3 with 14.92? Use the excerpt of the table below.

What are the degrees of freedom for the following table?

If the Null hypothesis is that cashiers at a particular franchise are twice as likely to be young adults as they are to be adults, and that they are just as likely to be adults as they are to be seniors, what is the chi square test statistic corresponding to that statistical test?

Young adults: 180
Adults: 85
Seniors: 135

Which of the following statements are true about the relationship between the p-value, $α$, and the null and alternative hypotheses?

What would not be appropriate null and alternative hypotheses in a test for a distribution of proportions in a set of categorical data?