Question

Pepsi claims that their diet drink tastes better than Coke's diet drink, and Melissa wanted to test this claim. So Melissa got a sample of 10 participants and asked them to rate how good each diet drink tasted on a scale of 0 (worst ever) to 10 (greatest ever). She also used non-labeled cups to reduce bias from participants. Use the data below to conduct a repeated-measures t-test using a non-directional hypothesis and an alpha of .05, and choose the correct t-values:

Participant	Diet Pepsi	Diet Coke
A	9	7
B	8	7
C	6	9
D	7	7
E	8	9
F	6	7
G	9	7
H	8	7
I	8	7
J	9	7

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d< 0

Alternative hypothesis: u_d > 0

Note that these hypotheses constitute a one-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = sqrt [ (\sum (d_i - d)² / (n - 1) ]

s = 1.645655

SE = s / sqrt(n)

S.E = 0.52068

DF = n - 1 = 10 -1

D.F = 9

t = [ (x₁ - x₂) - D ] / SE

t = 0.768

where d_i is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 9 degrees of freedom is more extreme than 0.768.

Thus, the P-value = 0.231

Interpret results. Since the P-value (0.231) is greater than the significance level (0.05), we have to accept the null hypothesis.

Do not reject H₀. From the above test we do not have sufficient evidence in the favor of the claim that diet drink tastes better than Coke's diet drink.