Is the chance of getting a cold influenced by the number of social contacts a pe

Question

Is the chance of getting a cold influenced by the number of social contacts a person has? A study by Sheldon Cohen, a psychology professor at Carnegie Melon University, seems to show that the more social relationships a person has, the less susceptible the person is to colds. A group of 276 healthy men and women were grouped according to their number of relationships (such as parent, friend, church member, and neighbor). They were then exposed to a virus that causes colds. A adaptation of the results is given in the following table.14 Number of Relationships 3 or fewer 4 or 5 6 or more 43 57 100 34 62 96 Cold No cold 49 31 Total 80

Explanation / Answer

here null hypothesis:Ho:susceptibility to colds and number of relationship are independent.

alternate hypothesis:Ha: susceptibility to colds and number of relationship are dependent.

degree of freedom =(rows-1)*(column-1)=(2-1)*(3-1)=2

for 2 df and 0.01 level of significance crtiical value =9.210

applying chi square test of independence:

as test statistic 12.182 is higher than critical value we reject null hypothesis

we have sufficient evidence at 0.01 level to conclude that  usceptibility to colds is affected number of relationship .

Observed OBS 3 or fewer 4 or 5 6 or more Total cold 49 43 34 126 no cold 31 57 62 150 Total 80 100 96 276 Expected Ei=?row*?column/?total 3 or fewer 4 or 5 6 or more Total cold 36.522 45.652 43.826 126 no cold 43.478 54.348 52.174 150 Total 80 100 96 276 chi square =(Oi-Ei)2/Ei 3 or fewer 4 or 5 6 or more Total cold 4.26 0.15 2.20 6.62 no cold 3.58 0.129 1.851 5.56 Total 7.84 0.28 4.05 12.182

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