(Iris) Below is a subset of data taken from the Iris dataset. We consider the sepal width and the species of Iris. Compute the rank sums for both species then compute the wilcoxon rank sum statistic

Sepal Width Species Rank
2 versicolor 1
2.2 versicolor 2
2.5 versicolor 3
2.6 versicolor 4
2.8 versicolor 5
2.9 setosa 6
2.9 versicolor 7
3 versicolor 8
3 versicolor 9
3 versicolor 10
3.1 setosa 11
3.1 versicolor 12
3.2 setosa 13
3.2 versicolor 14
3.3 versicolor 15
3.4 setosa 16
3.4 setosa 17
3.4 setosa 18
3.5 setosa 19
3.5 setosa 20
3.7 setosa 21
3.7 setosa 22
3.8 setosa 23
3.9 setosa 24
4.4 setosa 25
a)

n1:

n2:

W1:

W2:

W:

b) Recall that the wilcoxon rank sum test for two independent samples has less restrictions than independent t-tests when dealing with small sample sizes (hint we know from our probability material that the normal distribution can approximate sample means effectively when the sample size is less than 15, between 15 and 30 and greater than 30 when the underlying distribution is normal, symmetric, or skewed). Based on the two histograms of the full datasets for each population versicolor and setosa which test would you prefer the Wilcoxon rank sum test or an Indepednent t-test. Select the best answer

.

A)A wilcoxon ranks sum test as both population distributions appear to have a lot of skewness indicating that the underlying population distributions are not normal. Therefore an Independent t-test would not be valid as the sample sizes are both under 15.

B)An independent T-test as both population distributions appear to have a lot of skewness indicating that the underlying population distributions are not normal. As the sample sizes are both under 15 an Independent t-test would not be valid.

C)

Is it appropriate to use the normal approximation here? Compute the mean, standard deviation, and resulting p-value from the normal approximation for a two-sided wilcoxon rank sum test (round to four decimal places unless the answer is an integer).

Mw:

σW:

pval:

D)

Using the following web applet and the wilcoxon rank sum statistic computed previously compute the associated p-value. Round to four decimal places

https://homepage.divms.uiowa.edu/~mbognar/applets/wilcoxon-rank-sum.html

pval:

E)

At what significance level would your test conclusion for the normal approximation to the wilcoxon rank sum statistic be different than using exact two-sided p-values from a table of critical values or the above applet/numerical software.

a)0.0002

b)0.0005

c)0.005

d)0.001

F)

Based on the output above would you accept or reject the null hypothesis at the α=0.01 significance level. Provide a formal interpretation of the p-value and your conclusion of the test.

**I know this one is long I will leave good ratings!!**