Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size n1=24n1=24 with a mean of ¯x1=71.1x¯1=71.1 and a standard deviation of s1=18.6s1=18.6 from the first population. You obtain a sample of size n2=25n2=25 with a mean of ¯x2=78.6x¯2=78.6 and a standard deviation of s2=16.3s2=16.3 from the second population.

1. What is the test statistic for this sample?
2. What is the p-value for this sample?

Answer 1

Pooled standard deviation = Sqrt [ (n1-1) S²1 + (n2-1)S²2 / (n1 + n2 - 2) ]

= sqrt [ 23 * 18.6² + 24 * 16.3² / ( 24 + 25 - 2) ]

= 17.4634

Test statistics

t = (1 - 2) / [ sp * sqrt ( 1 / n1 + 1 / n2) ]

= (71.1 - 78.6) / [ 17.4634 * sqrt (1 / 24 + 1 / 25) ]

= -1.50

From T table,

With test statistics 1.50 and df of (n1 + n2 - 2) = 47,

p-value = 0.0702

Since p-value > 0.001, fail to reject H0