Question

Assume that the two samples are from a normal population. Please perform a t test for the differences in sample averages, indicating whether it is significant to 95% confidence (0.05 significance) using one and/or two sided. Assume that the population standard deviation is unknown but presumed equal. Show one-sided and two-sided actual Probability and Critical values using hand calculations and Excel

A 25 24 15 20 21 23 25 28 35 34

B 15 11 14 23 24 20 22 24 25 22

Answer 1

if test is one sided then the there is significant difference between A and B, as the one-tailed p-value=0.0471 is less than 0.05

if test is two sided then the there is not significant difference between A and B, as the two-tailed p-value=0.0941 is more than 0.05

here we use t-test with

null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1≠mean2 ( two tailed

statistic t=(mean1-mean2)/((sqrt(s1²/n1+s2²/n2))

with df =∆=

	sample	mean	s	s2	n	s2/n	(s2/n)2)/(n-1)
	Group1	25.0000	6.1101	37.3333	8	4.6667	3.111
	Group2	20.0000	4.8990	24.0000	8	3.0000	1.286
	difference=	5.0000	sum=	61.3333	16	7.666667	4.397
	df=	13.3682
	SE=	2.7689
	t=	1.8058
one tailed	p-value=	0.0471	two tailed	p-value=	0.0941
one tailed	critical t(0.05)	1.7709	two tailed	critical t(0.05)	2.1604