Note: Each bound should be rounded to three decimal...

Note: Each bound should be rounded to three decimal places. A random sample of n = 100 observations produced a mean of x? = 28 with a standard deviation of s = 3. (a) Find a 99% confidence interval for ? Lower-bound: Upper-bound: (b) Find a 90% confidence interval for ? Lower-bound: Upper-bound: (c) Find a 95% confidence interval for ? Lower-bound: Upper-bound:

Transcript

00:01 Hello students we are going to write here minus 28 and is 100 with standard deviation is 3 so basically if i write here for this we are going to find 99 % confidence interval for mu so basically if i write here for this confidence interval if i write here for this this must be x -war plus minus margin of error so basically i write here for this.

00:33 This is 28 plus minus we need to write here.

00:37 So this must be we need to write here 99 % confidence interval in the first case.

00:43 So this must be written as if i write here, this must be x alpha by 2 multiplied by as divided by under root of n, which is 28 plus minus z alpha y2 as 99 % percent.

01:01 Confidence interval is 2 .576 multiplied by 3 divided by under root of 100.

01:08 This is 28 plus minus 2 .576 multiplied by 3 divided by 10.

01:17 So basically if i write here, this must be 28 plus minus 7 .7 to 8.

01:26 So basically if i write here for this, this must be this must be.

01:29 This must be.

01:31 Written as we need to write here for this confidence interval is between we are going to write here 28 plus 7 .7 and 28 minus 7 .7 so basically if i write here for this this is again 28 minus 7 .7 so x bar value is between 28 plus 7 .7 which is 35 .7 28 minus 7 .7 if i write here this is 20 .3 so basically if i write here x bar value is between 20 .3 and 35 .7 so basically if i write here for this this must be our confidence interval confidence interval in the first case so this is 99 % confidence interval.

02:37 So basically if i write here, this is the answer in the first case.

02:41 So basically if i write here for this, this must be about b part.

02:45 So this must be, we need to write here for this lower bound, lower bound value is 20 .3 and upper bound value is 35 .7.

03:02 So let's erase this to make it more clear.

03:07 So basically if i write here for this, this must be erased.

03:11 So this is the answer in the first case.

03:14 Now our b part is we need to write here.

03:20 So this is for 90 % confidence interval.

03:29 Confidence interval...

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