Question

Xbar in the first sample: 2.3 Standard Deviation in the first sample: 2.4 Size of the first sample (n1): 13 Xbar in the second sample: 4.7 Standard Deviation in the second sample: 2.9 Size of the second sample (n2): 17

Use the conservative t-test to test the null hypothesis of equality of means. Submit the p-value of your test of significance.

Answer 1

H0: 1 = 2

Ha: 1 2

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

= sqrt [ 12 * 2.4² + 16 * 2.9² / 13 + 17 -2 )

= 2.6971

Test statistics  

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

= (2.3 - 4.7) / [ 2.6971 * sqrt( 1 / 13 + 1 / 17) ]

= -2.42

This is test statistics value.

For two tailed test,

p-value at 0.05 level with 28 df from T table = 0.0223

Since p-value < 0.05 level, we have sufficient evidence to reject H0.