Question

An industrial psychologist selected a random sample of seven young urban professional couples who own their homes. The size of their home (square feet) is compared with that of their parents (one-tailed test).

Couple Name	Professional	Parent
Gordon	1,725	1,175
Sharkey	1,310	1,120
Uselding	1,670	1,420
Bell	1,520	1,640
Kuhlman	1,290	1,360
Welch	1,880	1,750
Anderson	1,530	1,440

At the 0.05 significance level, what is the Wilcoxon signed-rank test value?

Compute the T value

At the 0.05 significance level, can we conclude that the professional couples live in larger homes than their parents? (one-tailed test)

Answer 1

d=Professional-Parent

Null hypothesis, H₀: Median of difference=0 vs. Alternative hypothesis, H₁: Median of difference>0

Arrange the values of d in increasing in magnitude:

70(-), 90(+), 120(-), 130(+), 250 (+), 250(+), 550(+)

Value of test statistic=T=sum of the rank of positive d's=2+4+5+6+7=24

p-value= 0.054>0.05

Hence we fail to reject H₀ at 5% level of significance.

There is insufficient evidence to conclude that the professional couples live in larger homes than their parents.