Question

Package 1	Package 2	Package 3
5014	5044	4944
4880	5095	5029
4877	5106	4914
4879	5053	5087
4868	5047	4887
5226	5049	4992
4871	4946	4897
4963	4897	4975
5097	4955	5183
5089	4895	4953
4957	5117	4960
4900	5061	4942

A company sells identical soap In three different packages at the same price. The sales of each package type for 12 months are listed above.

1. Use a=0.05, and construct confidence intervals for all pairs of differences between means. Which of these differences, if any, are statistically significant at the selected significance level? Are you surprised with your findings?

Answer 1

Note: the decision of null hypothesis rejection has been taken based on the modulus of test statistic since we are interested in the difference between the pairs in either direction i.e. Diff (1 - 2) and Diff (2 - 1) are same for us.

So, if | t | <= critical value, we have failed to reject the null hypothesis which was H₀: Pair-wise differences are zero. and the alternate hypotheses were H₁: Pair-wise differences are not equal to zero.

As per the analysis shown above, none of the pairs show any significant difference.

Computation