Question

Are beer, wine, and liquor consumed equally by Americans? A random sample found that out of 647 people, 293 selected beer, 218 selected wine, and 136 selected liquor.

1. What are the null and alternate hypotheses for the chi-square goodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Determine a chi-square test statistic and P value

4. Do you accept or reject the null?

Answer 1

(1)

Ho: The proportion of beer, wine and liquor consumption are equal. Pbeer= Pwine = Pliquor= 0.333

Ha: Some of the population proportions differ from the values stated in the null hypothesis

(2) Expected counts = 216

Category	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
beer	293	0.333	216	27.7300
wine	218	0.333	216	0.0252
liquor	136	0.333	216	29.4286
Total	647	1	647	57.1839

(3)

(sum of last coloumn in the above table)

df = 3-1 = 2

Level of significance = 0.05 (assuming 0.05 as the same is not mentioned)

p value = 0

(4)

critical = CHISQ.INV.RT(probability,df) = CHISQ.INV.RT(0.05,2) = 5.991

As the stat (57.1839) is greater than   critical, we reject the Null hypothesis.

Also as the p value (0) is less than level of significance, we reject the Null hypothesis.