00:01
In the first part, the sample mean is 21 .83, sample standard deviation, it is 7 .73.
00:08
The size is 82.
00:09
So we have ci 95 % and degrees of freedom between 82 minus 1, which is 81 and significance level is 0 .05.
00:18
So with this, df and significance level, if we calculate the t statistic value, that would be 1 .99.
00:30
So for 95 % confidence interval, if you calculate the expression, as you all know the formula x minus tc into s by under root n and x plus tc into s by under root n.
00:52
Right? this means 21 .83 minus 1 .99 into 7 .73 by under root 82 plus 1 .99 into 7 .73 by under root 82 plus 1 .99 into 7 .73 by under root 82.
01:19
So, if this all this we will get approximately 20 .132.
01:30
23 .8.
01:33
So this is the answer for a part.
01:37
Now if you see the b part, again the sample proportion p, it is given 0 .760.
01:48
763 and sample size we have 82 so we need to construct the 95 % confidence interval for the population proportion so here critical value is 0 .05 so the set c will be set 1 minus alpha by 2 that is 1 .96 now the corresponding confidence interval that would be p minus zc under root p into 1 minus p by n comma p plus zc under root p into 1 minus p by n so if we substitute all of these values 0 .763 minus 1 .96 under root 0 .763 into 1 .76 .0 .763 into 1 .763 into 1.
02:49
1 minus 0 .763 by 82 0 .763 plus 1 .963 plus 1 .96 under root 0 .763 into 1 .763 by 82.
03:20
This will be a confidence interval.
03:23
Let us calculate the values we will get 0 .671 comma 0 .855.
03:32
This is the final answer...