Question
Please show work
Suppose that experiment to see if taking vitamin C, vitamin D, or both, help prevent or reduce cold symptoms was conducted based on a random sample of 1981 individuals. Subjects were assigned to receive vitamin C only, vitamin D only, vitamin C and D, or placebo, and then were monitored for the duration of the cold season to see if they developed a cold or not. The results were tabulated in a two way table in which the column variables were the vitamin supplements and the row variables were the cold responses. Researchers then conducted a chi-square test for independence to see if cold responses and vitamin supplements are dependent. How many degrees of freedom does the chi-square statistic have? df = _______
Explanation / Answer
Let Oij represents observed frequencies for an individual who receiving jth treatment & in ith condition.
i=1,2 & j=1,2,3
Let r be the number of rows & l be the number of columns in above 2*2 table .
Here, r=2 & l=3.
Degees of freedom for test statistic is (r-1)*(l-1)=(2-1)*(3-1)=1*2=2
Thus, df=2
Vitamin A Vitamin B Vitamin A & B Cold O11 O12 O13 Not cold O21 O22 O23