00:01
We are asked to calculate the following confidence intervals for the sample from the normal population right.
00:11
So what is given to us is mean, sample mean is given to us which is x bar is equals to 35 and n is sample size which is 16 and sigma that is standard deviation is 7 right.
00:24
So what we know is that to calculate, to calculate a confidence interval, confidence interval for mu is, for mu when sigma is known as, known for the sigma is known okay is ci, confidence interval ci is equals to x bar plus z multiplied by sigma by root n.
01:12
This is the formula remember, this is the formula so you need to keep in mind.
01:17
Okay moving forward with that, we know the value of z.
01:26
So z could be also sometimes written as tc that is t statistics a critical value right but here i am also taking it z only right now.
01:38
So it would be given by x bar minus mu by sigma this is the formula.
01:42
So from here you will find out the value of z 35 minus, 35 minus mu that is but here remember that mu is not provided to us right.
01:58
So we are talking about the z score right from critical value we will find out the value for confidence interval right.
02:06
So for z is equals to 1 .96 you can say i am sorry z is equals to 1 .96 for 95 percent confidence interval.
02:35
So how you would find out because from degrees of freedom and alpha only alpha that alpha i am sorry alpha that is a significance level that from that only from these two conditions you can find out the value of z right.
02:51
So this is first condition second condition is z is going to be equals to 2 .576 perfect.
02:59
So for this is for 99 percent confidence interval that is correct right.
03:11
So now we will plug in these values here...