00:01
For this question, let me take notes here.
00:02
So the sample size, which was given as 44.
00:06
And be careful, the population standard deviation given here, that means we're going to use the z test.
00:11
And the sample size, which is 17 here.
00:15
So for part a, the confidence level was given as 90%, we can write as 0 .90.
00:22
And the confidence, so we're going to find the confidence interval for the mean.
00:25
So the confidence interval for mean, this is x bar plus or minus.
00:33
So we, because we have known the population standard division, we're going to use the z alpha over two times the population standard division and square root of the sample size.
00:43
Let's get the alpha value, which is one minus confidence level.
00:46
So the alpha over two, one minus 0 .90, divided by two, which is 0 .05.
00:52
So in order to get the z alpha over two, i'm going to use the inverse norm function for graphing display calculator.
00:58
This is 0 .05.
00:59
So the mean and the standard division for standard normal distribution, press second variance and the inverse norm, 0 .05 and zero, and then one.
01:08
So the value would be, which is negative 1 .64.
01:12
Let's put these values for the confidence interval.
01:16
44, this is plus or minus 1 .64 times.
01:20
So this population standard division and square root of 17 here, which is 44 plus 1 .64 and times the bracket, 6 divided by square root of 17 here.
01:34
So the upper boundary for the mean, this is 46 .39.
01:39
And for the lower boundary, i'm going to take the same number, just change the operation between them, which is 41 .61 here.
01:48
And what about for part b? in this case, the confidence level was given as 95%, which can be written as 0 .95...