Question

Can you conclude, using excel, that there is a real difference between X and Y? Use the appropriate hypothesis test. Use an alpha of 0.05. Be sure to clearly state the null and alternative hypotheses.

X 2.7579947 12.57883886 11.93286612 15.47061018 10.4145109 11.20388661 7.103587904 14.17643998 9.705847207

Y 16.11383372 12.21679045 12.54830756 11.77001117 9.905112875 10.5547892 10.12129959 12.2995907 14.4705887

Answer 1

Solution

Null Hypothesis H₀ =  There is a no real difference between X and Y

Alternative Hypothesis H₁ = There is a real difference between X and Y

so we will use two sample t test with equal variance

by using we will perform two sample t test and the output is

t-Test: Two-Sample Assuming Equal Variances
	X	Y
Mean	10.59384	12.22226
Variance	14.64079	4.13498
Observations	9	9
Pooled Variance	9.387884
Hypothesized Mean Difference	0
df	16
t Stat	-1.12743
P(T<=t) one-tail	0.138093
t Critical one-tail	1.745884
P(T<=t) two-tail	0.276187
t Critical two-tail	2.119905

Decision : Here p-value is greater than 0.05 level of significance hence we accept Null hypothesis and conclude that There is a no real difference between X and Y