Question

suomi A random sample of female students at a local university was selected. Each student reported her height (in inches), and then her height was actually measured. The results were as follows. 64 Reported height 62 66 67 61 69 60 63 68 65 70 Measured height 618 64.7 67 63.8 59.469.8 59.4 61.766.3 64.1 71.3 Difference 0.2 1.3 0 0.2 1.6 -0.8 0.6 1.3 1.7 0.9 -1.3 At the 0.10 level of significance, can we conclude (by using the Wilcoxon signed-rankstest) that there is a difference between the populations of reported and measured heights for female students at this university

Answer 1

Ans : The given results are

H₀: The median difference is zero versus

H₁: The median difference is not equal to zeo

the Wilcoxon Signed Rank Test

Reported height	Measured height	Difference	Sign	Rank	positive rank	negative rank
62	61.8	0.2	+	1.5	1.5
66	64.7	1.3	+	7	7
67	67	0
64	63.8	0.2	+	1.5	1.5
61	59.4	1.6	+	9	9
69	69.8	-0.8	-	4		4
60	59.4	0.6	+	3	3
63	61.7	1.3	+	7	7
68	66.3	1.7	+	10	10
65	64.1	0.9	+	5	5
70	71.3	-1.3	-	7		7

S1 = sum of positive rank = 44

s2= sum of negative rank = 11

Test Statistic :

W = min{S1,S2}

W = 11

test statistic is 11

to find critical value :

here n = 11 , $\alpha$ = 0.1

critical value = 14

Critical region : If | W | < W_critical then reject H0

Here W=11 <  W_critical then reject H0 at 0.1 level of significance

Vale of the test statistic	11
critical value	14
decision	Reject H0
at the 0.10 level , can we conclude that there is a difference between the population of reported and measured height for female students at this university	Yes