In: Statistics and Probability
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=22n1=22 with a mean of ¯x1=62.4x¯1=62.4 and a standard deviation of s1=15.3s1=15.3 from the first population. You obtain a sample of size n2=25n2=25 with a mean of ¯x2=55.3x¯2=55.3 and a standard deviation of s2=7.2s2=7.2 from the second population.
The test statistic is t assuming unequal variance
The value of test statistic is 1.991
P-Value is 0.0280
P-Value is greater than α
This test statistic leads to a decision to...fail to reject the null
As such, the final conclusion is that...There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.