Question

Dr. Shultz’s diet pills are supposed to cause significant weight loss. The table below shows the results of a recent study where 180 individuals took the diet pills and 120 did not. At the 5% significance level, test to determine if losing weight is dependent on taking the diet pills.

(a) Ho and Ha

(b) Test method, test statistic and p-value

(c) Statistical decision and case-specific conclusion

	Diet Pills	No Diet Pills	Total
No weight loss	80	20	100
Weight loss	100	100	200
Total	180	120	300

Answer 1

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H0: Losing weight is not dependent on taking the diet pills.

Alternative hypothesis: Ha: Losing weight is dependent on taking the diet pills.

We assume/given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 2

Degrees of freedom = df = (r – 1)*(c – 1) = 1*1 = 1

α = 0.05

Critical value = 3.841459

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Pills
Weight loss	Diet	No Diet	Total
NO	80	20	100
Yes	100	100	200
Total	180	120	300

Expected Frequencies
	Pills
Weight loss	Diet	No Diet	Total
NO	60	40	100
Yes	120	80	200
Total	180	120	300

Calculations
(O - E)
20	-20
-20	20

(O - E)^2/E
6.666667	10
3.333333	5

Test Statistic = Chi square = ∑[(O – E)^2/E] = 25

χ2 statistic = 25.00

P-value = 0.0000

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that losing weight is dependent on taking the diet pills.