Along the states of Maine, Florida, and Washington, there is a fishing industry

Question

Along the states of Maine, Florida, and Washington, there is a fishing industry that is subject to restrictions which regard to fishing in the water of those states. The restrictions contained banning U. S. lobsterers from fishing on the Bahamian portion of the water to the west of the Bahamas, where spiny lobster is prevalent. The purpose of the ban is to reduce the landings in, pounds per lobster pot from the average of 30.3 pounds prior to the ban. Below is a random sample of 20 lobster pots taken after the ban.

1. Run a t-test to determine whether there is significant evidence that the average landings per pot

decreased after the ban. Use a 5% significance level.

2. Run a Wilcoxon Signed-Rank test to determine whether there is significant evidence that the

median landings per pot decreased after the ban (assume that the median prior to ban was also

30.3 pounds). Use a 5% significance level.

3. Determine which of the tests should have been used.

10 12 13 14 16 18 20 weight 17.4 18.9 39.6 34.4 19.6 33.7 37.2 43.4 41.7 27.5 24.1 39.6 12.2 42.5 22 29.3 1.1 23.8 43.2 24.4

Explanation / Answer

We shall use the open source alternative R to solve this

the complete R snippet is as follows

weight<-c(17.4,18.9,39.6,34.4,19.6,33.7,37.2,43.2,41.7,27.5,24.1,39.6,12.2,42.5,22.1,29.3,21.1,23.8,43.2,24.4)

# t test
t.test(weight,mu = 30.3)

# non parametric alternative of t test
wilcox.test(weight,mu=30.3,alternative = "less")

The results are

> wilcox.test(weight,mu=30.3,alternative = "less")

   Wilcoxon signed rank test with continuity correction

data: weight
V = 104.5, p-value = 0.5
alternative hypothesis: true location is less than 30.3

> t.test(weight,mu = 30.3)

   One Sample t-test

data: weight
t = -0.23668, df = 19, p-value = 0.8154
alternative hypothesis: true mean is not equal to 30.3
95 percent confidence interval:
25.13225 34.41775
sample estimates:
mean of x
29.775

as the p value in both the cases is greater than 0.05 , hence we fail to reject the null hypothesis and conclude that there was no change in the average landings per pot after the ban

In order to determine which test to be used, lets check the normality assumption of the data, if the data is normally distributed then a t test would be fine , else a non parametric test

> shapiro.test(weight)

   Shapiro-Wilk normality test

data: weight
W = 0.92479, p-value = 0.1226

as the p value is greater than 0.1226 , hence we conclude that the data comes from a normal distribution, so a ttest should be used

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