00:01
In this problem, in first part, firstly, pivotal quantity for finding confidence interval for the population mean is pq is equal to x var minus muke over s over root n t n.
00:41
T n minus 1 where x var is mean that is 58 points and s is standard deviation that is 8 points and n is the sample size sample size that is 100 and mu is the population mean score of all new eras the third grade third graders we have to we have to construct a 95 % confidence interval for the population mean mu and p1 minus 1 .97 less than taa less than 1 .987, 0 .95.
02:08
Because critical value at 99 degree of freedom is plus minus 1 .987.
02:24
P minus 1 .987 less than x var minus mu over s over root n, less than 1 .987 is equal to 0 .95.
02:41
Now, p minus 1 .987 into s over root n, less than x var minus mu, less than 1 .987 into s over root n is equal to 0 .95.
02:59
This implies x var minus 1 .987 into s over over root n less than mu less than 1 plus less than x var plus 1 .87 into s over root n is equal to 0 .95.
03:26
Now 95 % confidence interval for mu is x var minus 1 .8 is x var minus 1 .8 .000.
03:42
Into s over root n x var plus 1 .987 into s over root n this is 56 .41 .59 .59 .59 .59.
04:02
Therefore a 95 % confidence interval for the mean score of all new jersey third graders is 56 .41 .59 .59 .59.
04:34
In second part, now same test is given to 200 randomly selected third graders, providing a sample average of 62 points and sample standard deviation of 11...