Question

The following represents a large, random sample of United Kingdom residents following their Brexit vote (withdrawal from the European Union). Age was broken down into three categories: 18-29, 30-59, 60 and older Individuals are coded as either stating that they voted for withdrawal or not. A. The following crosstable was produced: Age by Brexit 18-29 30-59 150 170 500 | 200 | 320 Total 880 870 1750 -60 240 Withdraw? Yes 490 No Tota 990 440

Answer 1

SOLUTION:

This is a case of Chi square test , we can quickly set this up in excel and check the p values using the chi square test function. The complete setup along with the formulaes is as shown below

Original 0 times 18-29 30-59 60 Total 18-29 30-59 60 Total 18-29 30-59 Total 150 170 320 170 150 320 200 240 4401750 Withdraw Yes 870 240 200 Withdraw Yes WithdrawYes 4900 5000 2400 2000 00 4400 17500 8800 No Total 1500 1700 3200 500 870 No 490 880 No 8700 1750 Total Total 18-29 30-59 60 Total 18-29 30-59 60 Total 18-29 30-59 Total WithdrawYes Withdraw Yes 870 880 4401750 Withdraw Yes 160.914 497.829 221.257 159.086 492.171 218.743 440 880 870 1750 159.086 492.171 218.743 160.914 497.829 221.257 1609.14 4978.28571 2212.57 8800 1590.86 4921.71429 2187.438700 9900 4400 17500 No No No Total 320 Total 320 Total 3200 Chi square Test 0.08499 Chi square Test 0.08499 Chi square Test 1.9669E-11

Original Yes No Total Age 18-29 150 170 320 30-59 490 500 990 60 240 200 440 Total 880 870 1750 Withdraw Age 18-29 -$F$13 C15/SF$15 SF$14*C15/SF$15 320 60 Total Yes No Total 30-59 -$F$13 D15/SF$15 $F$13 E15/SF$15 880 s$F$14*D15/$F$15 =$F$14*E15/SF$15 870 990 Withdraw 440 1750 Chi square Test -CHISQ TEST(C4 E5,C13 E14)

Reversed 18-29 170 150 320 30-59 500 490 990 60 200 240 440 Total 870 880 1750 Withdraw Yes No Total Total 18-29 s$M$13*115/$M$15-$M$13*K15/$M$15 s$M$14*115/$M$15-$M$14*K15/$M$15 320 30-59 60 -$M$13 L15/ŞM$15 870 SM$14 L15/SM$15 880 Withdraw Yes No Total 990 440 1750 Chi square Test -CHISQ. TEST(J4:L5,J13:L14)

10 times Age 18-29 1500 1700 3200 30-59 4900 5000 9900 60 2400 2000 4400 Total 8800 8700 17500 Withdraw Yes No Total Age 18-29 30-59 Total 60 =ST$13*S15/ST$15 8800 ST$14*S15/ST$158700 Withdraw Yes No Total -$T$14 Q15/ST$15 ST$14 R15/ST$15 3200 9900 4400 17500 Chi square Test -CHISQ.TEST Q4:S5,Q13:S14

we see that the p value does not change on reversing the rows of yes and no , however the p value does change when we multiply the values by 10.