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Q4) * Chi-Square Test for Independence (9 points total) *Thanks to one of the st

ID: 3227844 • Letter: Q

Question

Q4) * Chi-Square Test for Independence (9 points total)

*Thanks to one of the students in PSY230 for this research idea.

Another worker at Starbucks had a general impression from taking many, many drink orders that there might be a gender difference in terms of the type of drinks they order. Armed with the statistical learning she just learned from school, she decided to record the next 50 drink orders from female customers and 50 drink orders from male customers. The data are provided in the table below. The alpha level is .01.

Drink

Female

Male

Total count

Drip coffee

2

8

10

Hot espresso drinks

30

10

40

Cold espresso drinks

10

20

30

Iced coffee

4

12

16

Tea

4

0

4

Total count

50

50

100

a) State the null and alternative hypotheses in words (1 point each, 2 points total)

b) Calculate X2 statistic (1 for formula/work,1 for result, 2 points total)

c) Identify the critical value (1 point)

d) Compare the X2 statistic with the critical value (1 point)

e) Report the hypothesis test result, using “reject” or “fail to reject” in the answer (1 point)

f) Explain the conclusion in a sentence or two (1 point)

Drink

Female

Male

Total count

Drip coffee

2

8

10

Hot espresso drinks

30

10

40

Cold espresso drinks

10

20

30

Iced coffee

4

12

16

Tea

4

0

4

Total count

50

50

100

Explanation / Answer

a) State the null and alternative hypotheses in words (1 point each, 2 points total)

Answer :

Null Hypothesis : H0: There is no significant difference between genders and their drink preference.

Alternative Hypothesis : Ha : There is significant difference between genders and their drink preference at Starbucks.

b) Calculate X2 statistic (1 for formula/work,1 for result, 2 points total)

Observed Table

Expected Table

X2  = (2-5)2 /5 +  (8-5)2 /5 +  (30-20)2 /20 + (10-20)2 /20 + (10-15)2 /15 + (20-15)2 /15 +  (4-8)2 /8 + (12-8)2 /8 + (0-2)2 /2 +  (4-2)2 /2 = 24.93

c) Identify the critical value (1 point)

from chi- square table

X2critical for alpha = 0.01 and dF = (5-1) * (2-1) = 4 is X2critical = 13.277

d) Compare the X2 statistic with the critical value (1 point)

Here X 2 > X2critical so we can reject the null hypothesis and

e) Report the hypothesis test result, using “reject” or “fail to reject” in the answer (1 point)

We can reject the null hypothesis.

f) Explain the conclusion in a sentence or two (1 point)

We can conclude that there is significant difference between genders about their drink preference at Starbucks.

Drink Female Male Total count Drip coffee 2 8 10 Hot espresso drinks 30 10 40 Cold espresso drinks 10 20 30 Iced coffee 4 12 16 Tea 4 0 4 Total count 50 50 100