Question

5- Data for the ages of grooms and their brides for a sample of 10 couples were obtained. Couple 12345 6 78910 Groom Age 23 24 27 29 21 30 43 27 25 36 Bride Age22192424232637 222231 a) Conduct a statistical test to determine if there is a difference in mean ages of brides and grooms at significant level of 0.01. b) If the test had been done to determine whether the mean for groom was significantly larger than the mean for the brides. How would that change the alternative hypothesis and how you conduct the test'?

DO NOT use Excel for the question!

Answer 1

Ans:

	Groom	Bride	d
1	23	22	1
2	24	19	5
3	27	24	3
4	29	24	5
5	21	23	-2
6	30	26	4
7	43	37	6
8	27	22	5
9	25	22	3
10	36	31	5
		d-bar	3.5
		sd=	2.415

a)

$H_0:\mu _d=0$

$H_a:\mu _d\neq 0$

Test statistic:

t=(3.5-0)/(2.415/sqrt(10))

t=4.583

df=10-1=9

p-value(2 tailed)=tdist(4.583,9,2)=0.0013

As,p-value<0.01,we reject the null hypothesis and we can conclude that there is significant difference in mean ages.

b)

$H_0:\mu _d\leq 0$

$H_a:\mu _d>0$

p-value(one tailed)=tdist(4.583,9,1)=0.00066

As,p-value<0.01,we reject the null hypothesis and we can conclude that mean for groom was larger than the mean for brides.