11.1#4 The following table shows the Myers-Briggs personality preferences for a
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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.
(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.
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?
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 519Explanation / Answer
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.
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