To investigate how a person uses a mouse to click a targetedobject, a study recruits twelve people from each age group (young,middle and elderly) to take a mouse accuracy test. Withineach age group, there are six females and six males. All thirty-sixpeople have similar computer experiences with respect to using amouse. The test consists of a series of tasks that require clickingthe center of targets. The score of the test depends howquickly and accurately a person can hit the center of targets. Thefollowing table shows the scores of all thirty-six people, whichcan also be downloadedhere MouseAccuracy.csv Download .

	Female(j=1)	Male(j=2)
Young(i=1)	3211 2675 3154 2547 2762 3157	2704 2104 2955 2737 3004 2670
Middle(i=2)	2341 2472 2339 1914 1612 3001	2530 2373 2975 2138 2035 3070
Elderly (i=3)	2203 1930 1791 2716 1948 2892	1998 2230 1518 2486 1298 2479

Please notethat i and j i and j areindices that show the age group and gender group of people who takethe test.

Let j?ij denote the mean score for people who arein the ith age group and jth gendergroup.
Let ?i? denote the mean score for people who are inthe ith age group.
Let ??j denote the mean score for people who are inthe jth gender group.

Find 95% confidence interval for ?1??1?: lower limitis ? and upper limit is ? .
Find 95% confidence interval for ??2??2: lower limitis ? and upper limit is ? .
Find 95% confidence interval for ?31?31 : lowerlimit is ? and upper limit is ? .
Find 95% confidence interval for ??1???2??1???2: lowerlimit is ? and upper limit is ? .