00:01
Hello, we are given that the mean replacement time for a random sample of 20 washing machines is equal to 10 .1 years and the sample standard deviation is equal to 2 .2 years.
00:28
We want to construct a 95 % confidence interval for the population standard deviation of the replacement times of all washing machines of this type.
01:08
Now, the general equation for computing a confidence interval for a population population, population standard deviation is we have sigma or the standard deviation is greater than or equal to n minus 1 multiplied to the sample standard deviation squared divided by kai squared sub 1 minus alpha over 2 and this is, or sigma is less than or equal to n minus 1 times the sample standard deviation squared divided by kai squared sub alpha over 2.
02:13
Where what is kai squared sub alpha over 2 or 1 minus alpha over 2? this is the is the tabled critical table critical critical two -tailed value in the kai square distribution below which a proportion or a percentage equal to 1 minus alpha over 2 of the cases false now we are given that the confidence interval or confidence level is 95 % or 0 .95 so alpha which is equal to 1 minus cl is now equal to 0 .05 hence alpha over 2 is equal to 0 .05 all over 2 or 0 .025.
04:21
Therefore the confidence or 95 % confidence interval for the population standard deviation sigma is okay let me go back to our formula, go back to our formula.
05:07
We have a correction here.
05:09
It should be we should take the square root of this and also the square root of this.
05:16
Okay, so this is the general equation for the confidence interval of a population standard deviation.
05:24
So now we plug in the given to get the confidence interval.
05:31
So we have sigma is less than or equal to the square root of n minus 1.
05:43
So our n is 20.
05:45
So we have 20 minus 1 multiplied to the square of the sample standard deviation, which is 2 .2...