QUESTION 2 A mother of three children monitored how often her children cleaned t
ID: 3219839 • Letter: Q
Question
QUESTION 2
A mother of three children monitored how often her children cleaned their rooms over a one month period. The three children are ages 11, 9, and 6. They are named Angela, Victoria, and Charles, respectively. Angela's room was clean 21 days and messy 9 days. Victoria's room was clean 7 days and messy 23 days. Charlie's room was clean 14 days and messy 16 days. Use a chi-square to test the null hypothesis that child is unrelated to room status (messy/clean). What are the degrees of freedom for this test?
Explanation / Answer
Data:
n (Rows) = 3
n (Columns) = 2
Hypotheses:
Ho: The variables are unrelated, that is they are independent
Ha: The variables are related, that is they are dependent
Decision Rule:
= 0.05
Degrees of freedom = (3 - 1)(2 - 1) = 2
Critical Value = 5.991464547
Reject Ho if 2 > 5.991464547
Test Statistic:
2 = 8.14066092
p- value = 0.086559394
Decision (in terms of the hypotheses):
Since 8.14066092 > 5.991464547 we reject Ho
Conclusion (in terms of the problem):
It appears that the variables are related
Clean Messy Angela 21 9 Victoria 7 23 Charles 14 16