Question

In this question, we want to create a confidence interval for mu(m) - mu (u), the difference in average Income between the genders: Male and Female. You may use the original data for this, or notice that I’ve included two rows in addition to the Exam1 data which has the incomes broken down by gender.

a) Check the conditions to construct a confidence interval for the difference in these two means.

b) Include the output from Minitab or Statcrunch showing the confidence interval of interest.

c) Interpret the interval in words relating to the original question.

Age (Years) Education (Years) Gender Student Married Ethnicity Income (Dollars/Year) Income of Females Income of Males 71 14 Female No Yes Asian 29705 29705 18145 56 15 Male No Yes African American 18145 55412 49502 37 16 Female Yes Yes Caucasian 55412 20974 140672 44 16 Female No Yes Caucasian 20974 30550 13647 81 9 Female No No African American 30550 75406 103893 55 14 Male No Yes Caucasian 49502 12000 10635 46 9 Male No Yes African American 140672 30007 15741 41 14 Female No Yes Asian 75406 152298 44205 47 14 Male No Yes Caucasian 13647 87625 42529 28 14 Female No Yes Caucasian 12000 30682 17316 69 9 Female No Yes Caucasian 30007 31335 32856 41 12 Female No Yes Asian 152298 19782 60449 84 17 Male No No Asian 103893 130209 149316 69 16 Male No Yes Asian 10635 27470 11603 46 10 Female No No African American 87625 28575 83869 39 14 Male No Yes Asian 15741 34509 24050 77 7 Female No No Caucasian 30682 58351 107841 38 7 Female No No Caucasian 31335 15079 33017 46 16 Female Yes No Caucasian 19782 30413 29567 39 19 Female No Yes Caucasian 130209 80616 26370 32 12 Male No Yes Caucasian 44205 57337 24824 32 11 Female No Yes Asian 27470 94193 30012 37 11 Male No Yes Asian 42529 69165 36364 65 13 Male No No African American 17316 27369 15717 60 11 Female No No African American 28575 58929 30111 80 18 Female No Yes African American 34509 59879 35691 68 13 Male No No Caucasian 32856 44473 91362 69 8 Male No Yes Caucasian 60449 37878 28144 80 16 Male No No African American 149316 16103 52179 85 16 Female No Yes Caucasian 58351 53401 25124 71 11 Male No Yes Caucasian 11603 10588 68713 28 15 Female No Yes Asian 15079 31811 62328 83 11 Male No No African American 83869 26067 69656 32 18 Male No Yes Caucasian 24050 19537 44522 87 7 Male No No African American 107841 36496 71682 28 16 Male No Yes African American 33017 24230 16304 25 15 Female Yes No Asian 30413 23350 23793 25 15 Male No No Caucasian 29567 26532 23672 57 7 Female No Yes Asian 80616 29403 27229 78 11 Male No Yes Asian 26370 148924 60579 45 7 Female No No Caucasian 57337 22939 13561 33 9 Male Yes No Caucasian 24824 22561 53480 33 17 Male No Yes Caucasian 30012 106025 55882 44 16 Female No Yes Caucasian 94193 65896 28508 34 11 Female No No African American 69165 80861 12414 40 9 Female No Yes Caucasian 27369 29638 23949 66 9 Female No Yes African American 58929 15846 23857 78 15 Female No No Caucasian 59879 15333 14887 81 16 Female No No African American 44473 32164 16479 50 19 Male No No Caucasian 36364 20936 33437 38 16 Male Yes Yes Caucasian 15717 55187 125480 80 13 Female No No Caucasian 37878 59855 24889 81 18 Male No Yes Caucasian 30111 21455 36362 45 10 Female No Yes Caucasian 16103 14084 67937 35 15 Male No No African American 35691 41419 83851 47 17 Male No Yes Asian 91362 27272 25974 35 12 Female No No African American 53401 63931 43682 66 13 Female No Yes Caucasian 10588 40885 20405 75 13 Female No Yes Caucasian 31811 19144 64173 74 17 Female No Yes African American 26067 20089 35610 51 10 Male No Yes Caucasian 28144 27847 85425 57 14 Male No No Asian 52179 18951 91876 34 9 Female No Yes Asian 19537 49927 41400 29 12 Male No Yes Caucasian 25124 13676 76348 56 16 Male Yes No Caucasian 68713 98515 23012 83 15 Male No No Caucasian 62328 10735 15354 41 14 Male No Yes African American 69656 27794 160231 72 15 Male No Yes Asian 44522 58165 121709 57 16 Male No Yes Caucasian 71682 36508 68462 69 15 Female No Yes Asian 36496 73914 113772 66 10 Male No Yes Asian 16304 41025 21153 70 14 Male No No African American 23793 36934 41532 63 11 Male No No Caucasian 23672 134181 31367 51 11 Male No No Caucasian 27229 76782 38 15 Male No Yes Asian 60579 30733 64 15 Female No Yes Caucasian 24230 53308 49 12 Female Yes No Caucasian 23350 55054 58 19 Female No Yes Caucasian 26532 37 19 Male No Yes Asian 13561 83 15 Male No No Caucasian 53480 68 16 Male No Yes Caucasian 55882 56 14 Male No Yes Asian 28508 37 14 Female No Yes Caucasian 29403 36 11 Female No No Asian 148924 32 12 Male No Yes African American 12414 47 18 Female No Yes Asian 22939 40 18 Male No Yes African American 23949 56 16 Male No Yes Caucasian 23857 58 12 Male No Yes African American 14887 66 15 Female No No Caucasian 22561 82 15 Female Yes Yes Asian 106025 49 17 Female No Yes Caucasian 65896 29 15 Female No Yes Asian 80861 26 16 Male No No African American 16479 29 15 Female No Yes Asian 29638 44 9 Male Yes No Caucasian 33437 53 12 Female No No Caucasian 15846 82 16 Male No Yes Caucasian 125480 75 12 Male No Yes Caucasian 24889 47 9 Female No Yes Asian 15333 79 15 Female No Yes African American 32164 30 15 Female No No Asian 20936 50 17 Female No Yes Caucasian 55187 49 15 Male No Yes African American 36362 63 12 Male No Yes Asian 67937 47 18 Male No No Caucasian 83851 46 13 Female No Yes Caucasian 59855 24 10 Male No No Asian 25974 49 9 Male No Yes Caucasian 43682 72 17 Male Yes No Asian 20405 80 12 Female No Yes African American 21455 46 17 Female No Yes African American 14084 80 10 Male No Yes Caucasian 64173 40 12 Male No No Caucasian 35610 60 12 Male No Yes African American 85425 24 11 Female Yes No Caucasian 41419 33 10 Male No Yes Caucasian 91876 67 10 Female No Yes Caucasian 27272 36 14 Male No Yes Caucasian 41400 60 18 Male No No Asian 76348 28 14 Female No Yes African American 63931 81 16 Male No No Caucasian 23012 46 13 Female No Yes African American 40885 65 14 Male No No Asian 15354 69 17 Male No No Caucasian 160231 75 13 Female No No African American 19144 57 15 Female No Yes African American 20089 50 6 Male No Yes Caucasian 121709 78 15 Female No Yes Caucasian 27847 71 16 Male No Yes Caucasian 68462 82 13 Female No No Caucasian 18951 75 17 Female No Yes Caucasian 49927 69 15 Male Yes Yes Caucasian 113772 41 11 Male No No Caucasian 21153 50 12 Male No Yes Caucasian 41532 30 10 Male No Yes Caucasian 31367 44 12 Male No Yes Asian 76782 51 13 Male No No Caucasian 30733 80 16 Female No No African American 13676 78 11 Female No No African American 98515 44 17 Female No Yes Caucasian 10735 35 8 Female No Yes African American 27794 84 10 Male No Yes Caucasian 53308 56 12 Female No Yes Caucasian 58165 74 17 Male No Yes Asian 55054 79 6 Female No Yes Caucasian 36508 67 15 Female No Yes Caucasian 73914 79 19 Female No Yes Caucasian 41025 63 9 Female No Yes Caucasian 36934 48 13 Female No No Caucasian 134181

Answer 1

a) Check the conditions to construct a confidence interval for the difference in these two means.

1 ) here given sample of two data as male and female.

       And population standard deviation is unknown , since we use " t distribution "( t interval ) .

2) Check equality of variance :

So here P- value > 0.05 ; fail to reject H0.

Conclusion : At 5% level of significance we conclude there is sufficient eveidence to conclude that ,                   standard deviation for male and femal are equal .

Note : We use Pooled Variance t interval .

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Part b ) output from Minitab showing the confidence interval of interest.

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Part c ) Interpret the interval in words relating to the original question.

We 95% confidence that , a confidence interval for , the difference in average Income between the genders: Male and Female is lies between - 6937 to 14871 .