Wilcoxon Ranks Test (Weights data) In trying to educate the communities on healt

Question

Wilcoxon Ranks Test (Weights data)

In trying to educate the communities on healthy eating, researchers want to determine if weights recorded on packaged snack food items (popcorn, cookies, cakes, muffins, and pretzels) are accurate. The items are removed from its packaging and weighed on a high precision scale. Recorded package weights and obtained (actual) weights in ounces are given (see Weights dataset). The researchers would like to determine whether there was a difference in the weight between the two groups (Alpha = .05). For the purpose of this exercise, we will assume that at least one of the assumptions underlying the paired samples t-test is not tenable (i.e. that at least one of the variables is not normally distributed or that they do not have equal variances).

Write the research questions, null and alternative hypotheses and use the Wilcoxon Signed Ranks test to accept or reject the null hypothesis. Interpret the Ranks table. Write the results.

Research Question:

Research Hypotheses:

N

Mean Rank

Sum of Ranks

Recorded weights - Actual weights

Negative Ranks

17a

9.97

169.50

Positive Ranks

1b

1.50

1.50

Ties

2c

Total

20

a. Recorded weights < Actual weights

b. Recorded weights > Actual weights

c. Recorded weights = Actual weights

Test Statistics

Recorded weights - Actual weights

Z

-3.672b

Asymp. Sig. (2-tailed)

.000

a. Wilcoxon Signed Ranks Test

N

Mean Rank

Sum of Ranks

Recorded weights - Actual weights

Negative Ranks

17a

9.97

169.50

Positive Ranks

1b

1.50

1.50

Ties

2c

Total

20

a. Recorded weights < Actual weights

b. Recorded weights > Actual weights

c. Recorded weights = Actual weights

Explanation / Answer

The hypothesis formulation is as follows

H0 : there was no difference in the weight between the two groups

H1 : There  is a significant difference in the weight between the two groups

Interpretation :

We can see from the table 1 that 17 snacks had recorded weights less than the actual weights

1 instance where the recorded weight is more than the actual weight

and there are 2 instances where the recorded weight is equal to the actual weight.

Using the test statisitcs table

We are looking for the "Asymp. Sig. (2-tailed)" value, which in this case is 0.000. This is the p-value for the test. We report the Wilcoxon signed-ranks test using the Z statistic. As the p value is less than 0.5 hence we reject the null hypothesis in favor of altyernate hypothesis and conclude that There  is a significant difference in the weight between the two groups

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.