00:01
Okay, so we're told that the mean of the sample is 175 centimetres, that the size of the sample is 64, and we know the population standard deviation is 8.
00:11
So we want to first fill out this table in part a.
00:15
And so we need to fill out the z values for a 90%, 95 % and 99 % confidence interval.
00:23
And these are just the z values bounding the central 90%, 95 % and 99 % respectively.
00:29
And you can find from your z tables that that is 1 .64, 1 .96 and 2 .57.
00:37
The margin of error then as they say in the question is given by the z value that we just wrote down times sigma which here is 8 over the square root of n which here is 64.
00:51
8 over the square root of 64 is just 1 so we can see that this is just equal to z and so we just copy and paste those values again.
01:01
The interval then is given by, well the lower bound is given by the sample mean minus the margin of error, and the upper bound is given by the sample mean plus the margin of error.
01:13
And for these we find that we get 173 .36 to 176 .64 for the first one.
01:25
For the second one we get 173 .04 up to 176 .96.
01:32
And for the final one we get 171 .43 up to 177 .57.
01:44
For part b it says how does the confidence level change the margin of error if n and sigma remain the same? so we can see that the confidence level causes z to increase and therefore the margin of error to increase as well.
02:10
That increases the width of the interval.
02:12
And then for part c, we're asked what happens if we increase the sample size...