00:01
It is given that to examine the people's view on capital punishment, a survey is conducted on 1974 and 2006 and the contingency table from this is given below.
00:15
Year and the number of people who favored the punishment and the number of people who opposed the punishment and the total number of people surveyed.
00:27
For the year, 1974, the values are 9374 -473 -1410, and for the year 2006, the values are 1945870 -2815.
00:49
Let us represent the year 174 as population 1 and 2006 as population 2.
00:55
Now the option a is to find the proportion of people who favour the capital punishment in the year 1974, that is p1 cap equal to x1 by n1, where x1 is the number of people who favored the punishment in 1974 and n1 is the total number of people surveyed in 1974, that is 9377 by 141 317.
01:26
Simplifying this gives 0 .665 thus the proportion of people who favored the punishment in 1974 is 0 .665 now the option b is to find the proportion of people who favored the punishment in the year 2006 that is p2 cap equal to x2 by similarly as part a it is 1945 by 2815 simplifying this gives 0 .691 thus the proportion of people who favored the capital punishment in 2006 is 0 .691 now the part c is to construct the 90 percentage confidence interval for the proportion now these 90 percentage confidence level implies the 10 percentage significance level that is 0 .10.
02:32
Now using the excel formula of equal to minus norm dot s dot i nv significance level of 0 .10 divided by 2.
02:45
This gives the critical value.
02:48
The excel output is given below.
02:50
Using the excel output, the z critical value is 1 .6.
02:55
4 5.
02:57
Now the 90 percentage confidence interval is constructed as below.
03:01
That is p1 cap minus p2 cap plus or minus z critical value into root of p1 cap into 1 minus p1 cap divided by n1 plus p2 cap into 1 minus p2 cap into 1 minus p2 cap divided by n1 plus p2 cap into 1 minus p2 cap divided by by n2.
03:27
Now substitution of the values gives 0 .665 minus 0 .691 plus r minus 1 .645 into root of 0 .665 into 1 minus 0 .665 divided by 1410...