A researcher posits the following hypothesis: -Smoking cessation is independent

Question

A researcher posits the following hypothesis: -Smoking cessation is independent of nicotine patch use". After collecting data, he obtains the results below. Based on this data, you are to calculate the Chi-Square Test of Independence and determine statistical significance. Be sure to follow the steps and show your work!! Using the correct degrees of freedom determine the critical value of x^4 from Table 5 for alpha -0.05. What is the critical value for this test? (10%) Calculate the expected cell values. (25%) Calculate the Chi-Square Test of independence (show your work). (40%) Compare the obtained X^2 to the critical value: Is the difference statistically significant? How do you know? (10%) Summarize the result of the study in 1-2 sentences (include proportions, X^2, and p value). (15%)

Explanation / Answer

1) here degree of freedom =(row-1)*(column-1) =(2-1)*(2-1) =1

for 1 degree of freedom and 0.05 level ; critical value of chi square =3.8415

2,3) expected cell count and chi square independence test:

4) from above obtained chi sqaure value =5.3085 and p value =0.0212

5)here as test stat is greater then critical value and p value is less then 0.05 level of significance , we reject null hypothesis that smoking cessation is independence of nicotine patch use.

And conclude that smoking cessation is dependence of nicotine patch use.

Observed O Yes No Total Yes 81 72 153 No 51 79 130 Total 132 151 283 Expected E=rowtotal*column total/grand total Yes No Total Yes 71.364 81.636 153 No 60.636 69.364 130 Total 132 151 283 chi square =(O-E)^2/E Yes No Total Yes 1.301 1.137 2.439 No 1.531 1.339 2.870 Total 2.832 2.476 5.3085

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