00:02
The question is to obtain 95 % confidence interval for the population variance.
00:11
The formula to obtain the confidence interval for the population variance, that is sigma square, is n minus 1, s squared divided by kai square alpha by 2, is less than sigma square, is less than n minus 1, s squared divided by kai square 1 minus alpha by 2, where n is the sample size and s square is the sample variance.
00:58
The value of sample variance, that is s square, can be obtained by the formula, summation of xi minus x bar, whole bracket square, divided by n minus 1.
01:13
Where x bar is the sample mean therefore our first task is to obtain the value of sample mean which can be obtained by the formula summation x i upon n add all the observations given in the question and divide them by eight to obtain the value of sample mean that is x bar which is equals to 1 .09 divided by 8 therefore the value of x bar is 13 .625 now our next task is to obtain the value of sample variance that is s square we have already discussed the formula to obtain the value of sample variance is summation of x i minus x bar whole bracket square divided by n minus 1 this x i minus x bar whole bracket square is known as square deviation so the value of square deviation for the first data point can be obtained by substitute x i as a 14 and x bar as a 13 .625 and it's square which is equals to 0 .375 and its square which is equal to 0 .140625.
03:03
Similarly, obtain the value of s square for the other data point and add the values of x i minus x bar whole bracket square we get this summation as 49 .875.
03:28
Therefore, the value of s -square equal to 49 .875 divided by n -1, that is 8 -1.
03:50
Therefore, s -square equal to 49 .875 divided by 7.
03:59
Which is equal to 7 .125.
04:09
We know that the kai square distribution has a n minus 1 degrees of freedom.
04:15
Therefore, in this case, degrees of freedom can be obtained by n minus 1 which is equal to 8 minus 1 which is equal to 7.
04:27
We want to find the critical values that is kai square alpha by 2...