Question

EatWell Inc., a large fast-food chain company of Canada, wants to test two versions of a new product before launching its full production. They select a random sample of individuals among their regular clients and ask them to participate in an experiment to rate the product according to an assessment grid worth 20 points. The 15 individuals who accepted to participate had to come to a specific company location on two occasions during a given week to test the two versions of the product. It was a randomized experiment in which the version assigned to participants during their first visit was selected at random and participants did not know which version they were rating.

Individual   Version A   Version B
1   17   16
2   17   18
3   20   17
4   11   15
5   15   12
6   16   15
7   15   14
8   16   13
9   12   12
10   16   13
11   19   18
12   14   14
13   17   15
14   18   16
15   18   17

a) Comment on the distribution of the ratings for the two versions of the product and decide which statistical test is the most appropriate for this type of data. Justify your selection based on the assumptions and conditions required for the most appropriate test selected.

b) Regardless of your answer in a) above, perform a relevant parametric test using a 10% significance level to determine if there is a difference between the two versions of the product. Make sure you show your Minitab or other software output along with an interpretation of the results (manual calculations are not required here).

c) Now, perform a Wilcoxon signed rank test to verify if there is a significant difference at the 10% level between the two versions of the product based on these ratings. Show your manual calculations including the T+ and T- statistics and conclude based on the critical value approach.

d) Use Minitab or other software to perform the test in c) above and comment on the computed Pvalue and your conclusion in c). e) Compare your results from the parametric and non-parametric tests above and state what the final conclusion regarding the two versions of the product should be.

Answer 1

EatWell Inc., a large fast-food chain company of Canada, wants to test two versions of a new product before launching its full production. They select a random sample of individuals among their regular clients and ask them to participate in an experiment to rate the product according to an assessment grid worth 20 points. The 15 individuals who accepted to participate had to come to a specific company location on two occasions during a given week to test the two versions of the product. It was a randomized experiment in which the version assigned to participants during their first visit was selected at random and participants did not know which version they were rating.

Sample size (n) = 15

There are two versions version A and version B.

a) Comment on the distribution of the ratings for the two versions of the product and decide which statistical test is the most appropriate for this type of data. Justify your selection based on the assumptions and conditions required for the most appropriate test selected.

Here distribution of voth the versions is normal.

1. The data are continuous (not discrete).

2. The data follow the normal probability distribution.

3. The variances of the two populations are equal.

4. The two samples are independent. There is no relationship between the individuals in one sample as compared to the other.

5. Both samples are simple random samples from their respective populations. Each individual in the population has an equal probability of being selected in the sample.

SO here we use two sample t-test assuming equal variances.

b) Regardless of your answer in a) above, perform a relevant parametric test using a 10% significance level to determine if there is a difference between the two versions of the product. Make sure you show your Minitab or other software output along with an interpretation of the results (manual calculations are not required here).

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 is population mean for version A.

mu2 is population mean for version B.

Assume alpha = level of significance = 0.10

We can do this test in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Basic Statistics --> Two Sample t --> Each sample is in its own column --> Sample 1 : select version A data --> Sample 2 : Select version B data --> Options --> COnfidence level : 90.0 --> Hypothesized difference : 0.0 --> Alternative hypothesis : not= --> Assume equal variances --> ok --> ok

————— 13-02-2019 20:36:25 ————————————————————

Welcome to Minitab, press F1 for help.

Two-Sample T-Test and CI: Version A, Version B

Two-sample T for Version A vs Version B

N Mean StDev SE Mean
Version A 15 16.07 2.43 0.63
Version B 15 15.00 2.00 0.52

Difference = μ (Version A) - μ (Version B)
Estimate for difference: 1.067
90% CI for difference: (-0.317, 2.450)
T-Test of difference = 0 (vs ≠): T-Value = 1.31 P-Value = 0.200 DF = 28
Both use Pooled StDev = 2.2275

Test statistic = 1.31

P-value = 0.200

P-value > alpha

Accept H0 at 10% level of significance.

COnclusion : There is not sufficient evidence to say that two population means differs.

c) Now, perform a Wilcoxon signed rank test to verify if there is a significant difference at the 10% level between the two versions of the product based on these ratings. Show your manual calculations including the T+ and T- statistics and conclude based on the critical value approach.

Here we have to test the hypothesis that,

Test of median = 0.000000 versus median ≠ 0.000000

Test statistic W = 16.5

Mean difference = -2.23

sum of positive ranks = 74.5

sum of negative ranks = 16.5

Z-value = -2.0267

Mean (W) = 45.5

Standard deviation (W) = 14.31

Sample size (N) = 13

P-value = 0.04236

P-value < alpha (0.10)

Reject H0 at 10% level of significance.

Conclusion : There is sufficient evidence to say that median is differ than 0.

d) Use Minitab or other software to perform the test in c) above and comment on the computed Pvalue and your conclusion in c).

WIlcoxon signed rank test in MINITAB :

steps :

ENTER data into MINITAB sheet --> STAT --> Basic statistics --> Non parametrics --> 1-Sample Wilcoxon --> Variables : Version A - Version B --> COnfidence level : 90.0 --> Test median : 0.0 --> Alternative : not equal --> ok

Wilcoxon Signed Rank Test: Version A, Version B

Test of median = 0.000000 versus median ≠ 0.000000

N for Wilcoxon Estimated
N Test Statistic P Median
Version A 15 15 120.0 0.001 16.00

Version B 15 15 120.0 0.001 15.00

P-value = 0.0000

P-value < alpha

Reject H0 at 10% level of significance.

Conclusion : There is sufficient evidence to say that median is differ than 0.