A state superintendent is interested in determining if there is a relationship between the location of a school (Urban/Suburban) and students' proficiency in Math and Science. To investigate, the superintendent decides to use a Chi-Squared Test for Independence. Select the appropriate null and alternative hypothesis for the superintendent's test.

Which of the following shows a Chi-Squared Distribution?

Question 7 options:

Null Hypothesis: The level of proficiency in Math and Science is the same for both types of schools. Alternative Hypothesis: The level of proficiency in Math and Science is not the same for both types of schools.	A
Null Hypothesis: The location of a school and students' proficiency in Math and Science are independent. Alternative Hypothesis: The location of a school and students' proficiency in Math and Science are not independent.	B
Null Hypothesis: The level of proficiency in Math and Science is not the same for both types of schools. Alternative Hypothesis: The level of proficiency in Math and Science is the same for both types of schools.	C
Null Hypothesis: The location of a school and students' proficiency in Math and Science are not independent. Alternative Hypothesis: The location of a school and students' proficiency in Math and Science are independent.	D

Suppose that we would like to use the Chi-Squared Goodness of Fit Test to determine if the distribution of grades on a statistics test follows a normal "bell" distribution. Assume that a random sample of 200 exams were drawn and that the sample size is less than 10% of the population. You calculate the following expected frequencies:

Grade	A	B	C	F
Expected Count	34.72	42.46	50.54	72.28

Will we be able to use the Chi-Squared Goodness of Fit Test?

Yes, since all of the expected counts are greater than 30.

No, since all of the expected counts are smaller than 100.

Yes, since all of the expected counts are greater than 5.

No, since at least one of the expected counts is smaller than 5.

The contingency table below shows the results of a random sample of patients after being treated for an illness with a drug or a placebo.

	Drug	Placebo
Improvement	63	4
No Improvement	37	56

You want to determine if the distribution of the results (improvement/no improvement) is the same for both treatments. To do this, you use a Chi-Squared Test of Homogeneity. Determine the correct null and alternative hypotheses for this study.

Null Hypothesis: The results of the study are inconclusive.

Alternative Hypothesis: The results of the study are not inconclusive.