Question

11.1#4

The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and F refers to feeling.

	Personality Type
Occupation	T	F	Row Total
Clergy (all denominations)	52	96	148
M.D.	78	81	159
Lawyer	118	94	212
Column Total	248	271	519

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

#5

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Ceremonial Ranking	Cooking Jar Sherds	Decorated Jar Sherds (Noncooking)	Row Total
A	89	46	135
B	88	57	145
C	79	75	154
Column Total	256	178	434

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

Answer 1

R codes:

4. > tab=matrix(c(52,96,78,81,118,94),nrow=3,byrow=T) #entering the data into a matrix in R
> rownames(tab)=c("Clergy","M.D","Lawyer")
> colnames(tab)=c("Thinking","Feeling")
> tab=as.table(tab)
> tab
Thinking Feeling
Clergy 52 96
M.D 78 81
Lawyer 118 94
> chisq.test(tab) #Performing Chi-Square test

Pearson's Chi-squared test

data: tab
X-squared = 14.865, df = 2, p-value = 0.0005918
Since p-value < 0.05, we reject the null hypothesis of independence and conclude that there is a significant relationship between personality and occupation.

5. > tab=matrix(c(89,46,88,57,79,75),nrow=3,byrow=T)#entering the data into a matrix in R
> rownames(tab)=c("A","B","C")
> colnames(tab)=c("Cooking","Decorated")
> tab=as.table(tab)
> tab
Cooking Decorated
A 89 46
B 88 57
C 79 75
> chisq.test(tab) #Performing Chi-Square test

Pearson's Chi-squared test

data: tab
X-squared = 6.6233, df = 2, p-value = 0.03646
Since p-value < 0.05, we reject the null hypothesis of independence and conclude that there is a significant relationship between ceremonial ranking and pottery type.