Question

To test an assumption that boys are taller than their​ sisters, if I randomly select 13 boys who have sisters. The height of both the boys and their sisters in inches are below. Are boys taller than their​ sisters? I want to use a=0.05 level of significance and also need the p-value.

Height of Boys	Height of Sisters
67.5	72.6
68.8	72.3
67.6	70
69.5	71.4
66.9	68
70.1	70.8
72.5	72.6
70.2	69.7
70.7	69.4
72.6	70.8
72.3	69.8
73.1	69.5
66.7	61.6

Answer 1

let us consider

H0 : height of both the boys and their sisters are same

H1 : height of boys boys are taller than their​ sisters

putting the data in the minitab and using t test for two sample

we have

Two-sample T for Height of Boys vs Height of Sisters

N Mean StDev SE Mean
Height of Boys 13 69.88 2.28 0.63
Height of Sisters 13 69.88 2.85 0.79

Difference = μ (Height of Boys) - μ (Height of Sisters)
Estimate for difference: 0.00
95% lower bound for difference: -1.74
T-Test of difference = 0 (vs >): T-Value = 0.00 P-Value = 0.500 DF = 22

p value = 0.5

since p value is greater than 0.05 we accept the null hypothesis

i.e. we conclude that height of both the boys and their sisters are same.