00:01
So in question one, we're finding a z interval because the population standard deviation is known, and we want a 95 % confidence interval for a mean.
00:13
So we take the 9 for the x bar, plus or minus, and we use 1 .96 times the sample standard deviation, excuse me, the population standard deviation, which is 1 .2, and divided by the square root of 81.
00:28
And when we get that interval, it corresponds with letter c.
00:33
It is the 8 .74 hours to 9 .26 hours.
00:41
On question two, we're finding a 90 % confidence interval for a proportion.
00:51
So we're doing a one proportion, z interval.
00:54
And so we take the proportion plus or minus, and for 90%, we have, use 1 .645 and then divided by the standard air and the standard air is 0 .23 times its complement which is 0 .77 and then divided by the sample size and the sample size was 500.
01:15
And when we get that, the answer comes out to be your letter a.
01:20
It is 0192 .261.
01:28
For question 3, we're finding a t interval because we don't know the population standard deviation.
01:37
It's a 99 % confidence interval for the mean.
01:43
And so we take the x bar of 22 .5 plus or minus.
01:49
And then we had to have a t value that has 0 .005 in the upper tail.
01:54
And we had to have, let's see, 53 degrees of freedom...