00:01
Hello, here in part a, we have our size of the sample mean and is equal to 60, and our sample mean x bar is 80, and our population standard deviation, sigma is given is equal to 15.
00:11
So we have sigma sub x bar here.
00:13
The standard error of the mean is given by sigma over the square root of n.
00:17
So therefore, that's going to be equal to 15 over the square root of 60, which is going to be equal to approximately 1 .94.
00:28
And then for a 95 % confidence, well, the confidence coefficient here is 1 minus alpha, which is 0 .95, and alpha is 0 .05.
00:40
So we then get from our probability table that z sub 0 .025 is equal to 1 .96.
00:48
So to obtain a 95 % confidence, we want 80, which is x bar, plus or minus 1 .9.
00:58
96 times 15 over the square root of 60, which gives us 80 plus or minus 3 .8.
01:08
So the 95 % confidence interval is 80 minus 3 .8, which is 76 .2 to 80 plus 3 .8, which is 83 .8.
01:17
Therefore, our confidence interval goes from 76 .2 to 83 .8.
01:28
And then for part b, we have that our sample size now is n equal to 20.
01:33
Sample mean, x bar is 80...