Question

In a survey about student’s smoking habit, the following results were obtained from 236 randomly selected students:

   Heavy-smoker Non-smoker Occasional-smoker Regular-smoker
   11                189            19               17

Suppose the campus smoking statistics is believed to be as shown below. Determine whether the sample data is consistent with the campus smoking habits at α=0.05 significance level.   Use an appropriate exact non-parametric goodness of fit test as well as an approximate Chi-square goodness of fit test.

   

   Heavy-smoker Non-smoker Occasional-smoker Regular-smoker
      4.5%         80%            8.5%            7%


If you could state what type of test was used for the first part, that would be very helpful as well. Thanks!

Answer 1

The Chi-square goodness of fit test is used here.

The hypothesis being tested is:

H0: The sample data is consistent with the campus smoking habits

Ha: The sample data is not consistent with the campus smoking habits

observed	expected	O - E	(O - E)² / E
11	10.620	0.380	0.014
189	188.800	0.200	0.000
19	20.060	-1.060	0.056
17	16.520	0.480	0.014
236	236.000	0.000	0.084
.08	chi-square
3	df
.9937	p-value

The p-value is 0.9937.

Since the p-value (0.9937) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the sample data is consistent with campus smoking habits.