Question

Gretchen wants to know whether gender has a relationship to beverage choice among her coworkers. She defines beverage choice as the first beverage consumed upon arrival at work and selects a random sample of her coworkers. She records her coworkers' consumption habits one morning and the results are shown in the table. Is there sufficient evidence at the 0.05 level to say that gender and beverage choice are related?

Observed Sample of 90 Coworkers:

	Coffee	Tea	Water	Other	Total
Male	10	7	18	9	44
Female	8	12	11	15	46
Total	18	19	29	24	90

1.  State the hypotheses for this test

2. Determine the number of females whose first choice was expected to be water.
Possible Answers: A: 9.92 B: 20.3 C:14.82 D:11.0

3. Compute the value of the X² test statistic.
Possible Answers: A:  0.196 B: 4.686 C: 10.773 D: 11.212

4. State the conclusion of this hypothesis test.
Possible Answers: A: Reject H0. There is enough evidence to support the claim that gender and beverage choice are related.
B: Fail to reject H0. There is not enough evidence to support the claim that the means of the two genders are the same.
C: Reject H0; There is enough evidence to state that females prefer to drink tea.
D: Fail to reject H0. There is not enough evidence to support the claim that gender and beverage are related.

I need help walking through the steps - I am making errors along the way, don't have too many issues with 1&4 but the middle is a little iffy.

Answer 1

Chi-Square Test

Observed Frequencies(fo)
	Column variable						Calculations
Row variable	coffee	tea	water	other	Total		fo-fe
male	10	7	18	9	44		10-8.8=1.2000	-2.2889	3.8222	-2.7333
female	8	12	11	15	46		-1.2000	2.2889	-3.8222	2.7333
Total	18	19	29	24	90
Expected Frequencies(fe) = Σrow*Σcolumn/Σtotal
	Column variable
Row variable	coffee	tea	water	other	Total		(fo-fe)^2/fe
male	18*44/90=8.80	19*44/90=9.29	29*44/90=14.18	24*44/90=11.73	44		0.1636	0.5640	1.0304	0.6367
female	18*46/90=9.20	19*46/90=9.71	29*46/90=14.82	24*46/90=12.27	46		0.1565	0.5395	0.9856	0.6091
Total	18	19	29	24	90

1)

Ho:gender and beverage choice are not related

H1:gender and beverage choice are related

2)

Expected Frequencies(fe) = Σrow*Σcolumn/Σtotal

the number of females whose first choice was expected to be water =29*46/90=14.82

3)

X² test statistic.=Σ(fo-fe)^2/fe =0.1636 + 0.5640 + 1.0304 + 0.6367 +0.1565 + 0.5395 + 0.9856 + 0.6091 = 4.686

4)

DF=(row-1)(column-1)=1*3=3

chi square critical value=7.81473 [excel formula =chisq.inv.rt(0.05,3)

since, test stat <critical value, do not reject Ho

hence, answer is

Fail to reject H0. There is not enough evidence to support the claim that gender and beverage are related