00:01
Hello students, here from the question they given that a well -known iq test with a mean of 100 was used to access intelligent.
00:14
So here they given that the population mean mu which is equal to 100.
00:20
Then a group of 40 10 years old.
00:23
So here our sample size n which is equal to 40 and the sample mean x bar which is equal to 82 and then the sample standard deviation s which is equal to 16.
00:50
They given the confidence level as 95 percentage.
00:54
So alpha which is 1 minus 0 .95 we get 0 .05.
01:00
Then for the subpart a what is the 95 percentage confidence interval.
01:05
Then for the subpart a the formula for calculating the confidence interval which is x bar plus or minus t critical value into s by square root of n.
01:15
The t critical value which is t alpha by 2 comma n minus 1 degrees of freedom.
01:21
So here the t critical value which is t 0 .05 by 2 comma 39 degrees of freedom.
01:29
We get the critical value as 2 .02.
01:38
Now substitute the known values the confidence interval which is equal to 82 plus or minus 2 .02 into 16 divided by the square root of 40...