Question

1) Preform the Signed Test to test if the  data below has a median of 30

2)  Preform the Signed Ranked Test to test if the data is symmetric around its mean

30.1, 32.7, 22.5, 27.5 27.7, 29.8, 28.9, 31.4 31.2, 24.3, 26.4, 22.8 29.1, 33.4, 32.5, 21.7

Answer 1

Sign Test

Ho: Median is equal to 30

H1: Median is not equal to 30

Observation	Median
30.10	30.00
32.70	30.00
22.50	30.00
27.50	30.00
27.70	30.00
29.80	30.00
28.90	30.00
31.40	30.00
31.20	30.00
24.30	30.00
26.40	30.00
22.80	30.00
29.10	30.00
33.40	30.00
32.50	30.00
21.70	30.00

Frequencies
		N
Median - observation	Negative Differencesa	6
	Positive Differencesb	10
	Tiesc	0
	Total	16
a. Median < observation
b. Median > observation
c. Median = observation

Test Statisticsa
	Median - observation
Exact Sig. (2-tailed)	.454b
a. Sign Test
b. Binomial distribution used.

Here p value is .454 which is greater than 0.05 , hence we fail to reject the null hypothesis and conclude that median is equal to 30.

Wilcoxon Signed Ranks Test

H0: Data is symmetric about its mean

H1: data is not symmetric about its mean

observation	Mean
30.10	28.25
32.70	28.25
22.50	28.25
27.50	28.25
27.70	28.25
29.80	28.25
28.90	28.25
31.40	28.25
31.20	28.25
24.30	28.25
26.40	28.25
22.80	28.25
29.10	28.25
33.40	28.25
32.50	28.25
21.70	28.25

Ranks
		N	Mean Rank	Sum of Ranks
Mean - observation	Negative Ranks	9a	7.83	70.50
	Positive Ranks	7b	9.36	65.50
	Ties	0c
	Total	16
a. Mean < observation
b. Mean > observation
c. Mean = observation

Test Statisticsa
	Mean - observation
Z	-.129b
Asymp. Sig. (2-tailed)	.897
a. Wilcoxon Signed Ranks Test
b. Based on positive ranks.

P value is .897 , Hence we fail to reject the null hypothesis and conclude that data is symmetric about its mean