Is the type of beverage ordered with lunch at a restaurant independent of the ag
ID: 3314716 • Letter: I
Question
Is the type of beverage ordered with lunch at a restaurant independent of the age of the consumer? A random poll of 309 lunch customers is taken, resulting in the following contingency table of observed values. Use a=0.05 to determine whether the two variables are independent.
Preferred Beverage
Age
Coffee/Tea
Soft Drink
Other
(Milk, etc)
Total
21 – 34
26
95
18
139
35 – 55
41
40
20
101
>55
24
13
32
69
Total
91
148
70
309
Count
Expected
Cell Chi^2
Coffee/Tea
Other(Milk, Etc.)
Soft Drink
Total
>55
24
20.3204
0.6663
32
15.6311
17.1416
13
33.0485
12.1622
69
21-34
26
40.9353
5.4491
18
31.4887
5.7781
95
66.5761
12.1353
139
35-55
41
29.7443
4.2593
20
22.8803
0.3626
40
48.3754
1.4501
101
Total
91
70
148
309
(a). Test the null hypothesis by using Chi-square test.
(b). Test the null hypothesis by using p value
Preferred Beverage
Age
Coffee/Tea
Soft Drink
Other
(Milk, etc)
Total
21 – 34
26
95
18
139
35 – 55
41
40
20
101
>55
24
13
32
69
Total
91
148
70
309
Tests N DF LogLike RSquare (U) 0.0912 309 4 29.562725 Test Likelihood Ratio Pearson Chisquare Prob> Chisq 59.125 59.405Explanation / Answer
a)
As per chi-square test, chi-square = sum((Oi - Ei)^2/Ei) = 59.4047
Critical value of chi-square = 9.48 ( =CHISQ.INV.RT(0.05,4))
Reject the null hypothesis as calculated value is greater than critical value.
b)
p-value = 0.0000 < 0.0001
Reject the null hypothesis as p-value is less than significance level of 0.05
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