00:01
Let us represent x as the time spent watching television using dvr and it is given that x follows normal distribution with standard deviation of sigma equal to 4 .3 minutes.
00:18
And in the first part we have to construct a 95 percentage confidence interval.
00:24
Since the population standard deviation sigma is given the z distribution.
00:30
Is used to construct the confidence interval and the mini tab procedure for constructing confidence interval is given below first enter the data in the excel and then second step is to select the stat and then select basic statistics and then select one sample z and then select the variable using the select option and then in the box known standard deviation in short sd enter 4 .3 and then select the options then select confidence level in short c l enter that as 90 and in 9th step select okay and then select okay the mini tab output is given below using the mini tab output the 90 percentage conference interval is 90 percentage conference interval is 23 .862 now the width of the interval is calculated as upper confidence level minus the lower confidence level, that is subacting 23 .862 from 26 .253, which gives 2 .391.
02:24
In second part we have to construct the 99 % confidence interval and the miniatab are same for the first 1 to 10 step.
02:36
The changes in the 8th step is for the confidence level we have to type 99 and the minotap output is given below.
02:47
Now using the minotap output the 99 % confidence confidence confidence.
02:54
Interval is 23 .185 comma 26 .929 minutes and the width is calculated by subacting 23 .185 from 26 .929.
03:16
This gives 3 .7 .4.
03:21
Now the 90 percentage confidence interval have the width.
03:26
Of 2 .391 and 99 percentage confidence interval have the width of 3 .7 -4...