Is the null hypothesis that the following population data fo

Is the null hypothesis that the following population data for group A, 59, 44, 56, 48, 39, 62, 48, 37, 65, 63, 47, has the same mean as data for group B, 68, 82, 68, 76, 69, 77, 70, 64, 81, 69, 78, true or false according to a one-tailed test assuming the group A\'s mean is less than group B\'s mean with an alpha level of 0.05.

True or False?

Solution

This is comparison of means of two samples A and B

Create null and alternate hypothesis as:

H0: mu1 = mu2

Ha: mu1 < mu2

Sample sizes n1 = 11 and n2 = 11

As sample size is small t test can be done.

The mean of Group One minus Group Two equals -21.55
  95% confidence interval of this difference: From -28.71 to -14.38
t = 6.2686
  df = 20
  standard error of difference = 3.437

p value = 0.00005

As p <0.05 difference is highly significant between A and B.

Hence null hypothesis is rejected and there is statistical evidence to the claim that mean of A < mean of B.