Question

A) If we wanted to determine whether the effectiveness of a vaccine (two outcomes: succeed vs. fail) depends on blood type, what type of test should we conduct?

Regression

z test

chi square test of independence

F test

t-test

goodness of fit test

B) Suppose that we run a Chi Square test and find a Chi Square value of 8 with 8 degrees of freedom. What is the p value?

		.3449
		.4335
		.5178
		.05
		.1845
		.9999

C) Suppose that we wish to test the effect of caffeine on working memory performance in an "AB" design with 100 participants. That is, half of the participants get caffeine on day 1 but have no caffeine on day 2. The other half the participants do the opposite: no caffeine on day 1 then caffeine on day 2. We then test whether each person was able to remember all the tasks they were assigned for that day (pass/fail). In a within-subjects design like this, would a Chi Square test be appropriate?

		a) No. For a Chi Square test, each participant must contribute data to only one cell. The above design violates this key assumption.
		b)No. You can't use a Chi Square test when there are only two outcomes (pass vs. fail).
		c)Yes, assuming it is reasonable to characterize performance as Pass vs. Fail (i.e., whether it is truly dichotomous)
		d) Yes. The Chi Square test of independence is in fact ideally suited to such a situation.

D) Suppose we have data on the number of employees in "people-oriented" jobs (like clinical psychology and nursing) vs. "thing-oriented" jobs (like electrical engineering and oil rigs) and whether each is male or fame. We then conduct a chi-square test of independence to determine whether sex and job type are statistically related. What is the null hypothesis of the test?

		males have higher salaries than females
		each job type (people vs. things) is equally common
		job type and sex are dependent
		men prefer jobs about things
		sex and job type are independent
		men and women are equally likely to work

Answer 1

A)

If we wanted to determine whether the effectiveness of a vaccine (two outcomes: succeed vs. fail) depends on blood type, what type of test should we conduct?

"chi square test of independence"

Chi-square test of independence: It is used to determine if there is statistically significant association / dependence / relation between two categorical variables (or attributes).

Attribute-1: Two outcomes Success/Fail
Attribute-2: Blood type
[Blood group may be A/B/O/AB]
Null Hypothesis-H0: Effectiveness of vaccine does not depend on Blood type.
Alternative Hypotheis-H1: Effectiveness of vaccine depends on Blood type.

B)

Suppose that we run a Chi Square test and find a Chi Square value of 8 with 8 degrees of freedom. What is the p value?
# p-value=P(chi-square > chical)
# chical=calculated value =8
# "pchisq()" is the command in R-software which gives the value of probability P(X<=x), where X is chi-square random variable.
pval=1-pchisq(8,8)
pval
[1] 0.4334701
round(pval,4)
[1] 0.4335