Question

You are an analyst for the Coral Cola Company and are interested in the association between age and rating of a new type of soda (Irish-Cream Cream-Soda). You suspect that younger individuals will prefer the soda over older individuals which could be useful for developing advertisement programs that can appeal to the population that likes Irish-Cream Cream-Soda the most (e.g., younger individuals). You conduct a study in which you allow participants (n = 15) to taste the new soda and rate how much they like it on a scale from 1 – 10 (1 being the “worst thing I ever tasted” to 10 being the “best thing I ever tasted”). In addition, you record their age. Use the 6 steps of hypothesis testing and SPSS to determine whether there is an association between ratings of Irish-Cream Cream-Soda and age. The data is provided below. Conduct the appropriate statistical test either by hand or via SPSS (listed at the bottom), record your answers on the answer sheet, and attach SPSS output.

ID	Age	Rating
1	48	1
2	48	4
3	26	8
4	24	3
5	24	7
6	23	10
7	23	9
8	33	6
9	33	5
10	30	5
11	29	5
12	26	10
13	41	3
14	40	2
15	35	3

a) State (0.5 pt) and calculate (0.5 pt) an acceptable measure of variability for Age? (1 pt)

b) What is the appropriate statistical test to answer question? (0.5 pt)

c) Step 1: What is your prediction regarding the results of the statistical test? (0.5 pt)

d) Step 2: Set up hypotheses (2 pts)

H₀ (1 pt):   

H₁ (1 pt):   

e) Step 3: Set criteria for decision (2 pts)

Critical value (1 pt):

Decision Rule (1 pt):   

f) Step 5: Report Results (2 pts) – Must include test statistic (0.5 pt), degrees of freedom (0.5 pt), p-value (0.5 pt), and appropriate measure of effect size (0.5 pt)

g) Step 6: Interpret the results of the statistical test in terms of the research question (1 pt)

SPSS DATA
(First Section = Age)
(Second Section = Rating)
48   1
48   4
26   8
24   3
24   7
23   10
23   9
33   6
33   5
30   5
29   5
26   10
41   3
40   2
35   3

Answer 1

a)The acceptable measure of variability for Age will be Sample Standard Deviation (s) :

=8.628855

b)The appropriate test will be : Correlation test.

c) Prediction is there may be correlation between age and ratings since as age increases, the person becomes critical of some food. (psychological thing it happens)

d) Here, null hypothesis is H₀: =0 and the alternative hypothesis is H₁: not H₀,
where = Population correlation coefficient between age and ratings.

e)Critical value : t_{0.05/2; n-2} = t _0.025;13 = 2.16
Decision Rule : Reject H₀ if | Test Statistic T | > 2.16

f) Here, Correlation between age and ratings r = -0.74093.
Test Statistic :

= -3.97781
Degrees of freedom : DF = n-2 = 13
p-value : , where t₀ = Observed value of T

, since T ~ t_n-2 under H₀

= 0.001576632

g) Since p-value < 0.05, we reject H₀ and conclude that there is significant linear association between age and ratings.