00:01
Hello students, in the first question we have to determine what is the change in the length of the confidence interval by the confidence level.
00:09
So, first we have given the 95 % confidence interval for the population mean.
00:15
So, that means we have confidence level c is equal to 95%.
00:19
Therefore, significance level alpha is 1 minus c that is equal to 1 minus 0 .95 is equal to 0 .05 and therefore, we will get the value of z alpha by 2 that is the critical value which is equal to z 0 .025 is equal to 1 .96 this is by using the z table.
00:44
Then next we have the confidence level c is equal to 99%.
00:49
Therefore, alpha is 1 minus c that is equal to 1 minus 0 .99 is equal to 0 .01.
00:58
Therefore, z alpha by 2 is equal to z 0 .005 and that is equal to 2 .576.
01:07
This is also by using the z table and here we can observe that the critical value of 99 % is greater than the critical value of 95%...