Question

An oceanographer believes that the median height of the waves at Ocean City is 2.8 feet. The wave heights are measured for a random sample of 20 days. The data are as shown here. At , is there enough evidence to reject the oceanographer’s claim?

3.6	2.1	2.3	2.1	2.7
3.2	3.9	3.4	3.0	2.9
2.0	1.9	3.2	3.5	2.8
1.8	2.3	3.7	3.9	4.2

1. Test for Normality.
2. State a null and alternative hypothesis for a parametric and a nonparametric test.
3. Give your decision from both tests and a final conclusion.

Answer 1

Ho: data is normal

H1: data is not normal

Shapiro-Wilk Test
	3.6
W-stat	0.946107
p-value	0.338562
alpha	0.05
normal	yes

conclusion: data is normal

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for non parameteric

H0:median=2.8 ( claim ),

H1:median not equal 2.8

signed test

x1	x2	difference
3.6	2.8	0.8
3.2	2.8	0.4
2	2.8	-0.8
1.8	2.8	-1
2.1	2.8	-0.7
3.9	2.8	1.1
1.9	2.8	-0.9
2.3	2.8	-0.5
2.3	2.8	-0.5
3.4	2.8	0.6
3.2	2.8	0.4
3.7	2.8	0.9
2.1	2.8	-0.7
3	2.8	0.2
3.5	2.8	0.7
3.9	2.8	1.1
2.7	2.8	-0.1
2.9	2.8	0.1
2.8	2.8	0
4.2	2.8	1.4

total negative sign = 8

total positive sign = 12

n=20

test statistic = min (8,12) = 8

p value= 2*P(X≤6) = 2*BINOM.DIST(8,20,0.5,TRUE) = 0.5034

since, p value >α=0.05, fail to reject Ho

hence, there is no enough evidence to reject the claim that median is 2.8

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