00:01
For this problem, we are told that a sample of fat content in percentage of n -equals 10 randomly selected hot dogs results in a sample mean of 21 .9 and a sample standard deviation of 4 .134.
00:12
So we have x bar equals 21 .9 and sample standard deviation s equals 4 .134.
00:23
Then we're asked that assuming that the hot dog fat content follows a normal distribution, we are to compute and interpret a 95 % confidence interval for the true mean hot dog fat content.
00:37
So i'll treat that as that is part a there.
00:41
So we have that our confidence interval is going to be given by x bar plus or minus the standard error here.
00:49
The standard error is going to be given by the, or pardon me, i'm getting ahead of myself here.
00:55
It would be x bar plus or minus t of 0 .025 for nine degrees of freedom because n equal.
01:01
10.
01:02
And because we're using the t distribution because we have a small n and we don't know the population standard deviation.
01:10
So it would be t 0 .0259 times s over the square root of n.
01:18
So let's see here.
01:22
Let's take x bar is 21 .9 and then we'd want to have this plus the negative of, can do the negative of 2 .262 times standard deviation 4 .134 over the square root of n, so square root of 10, or plus 2 .62, etc.
01:53
So we find that the lower end of the confidence interval is going to be 18 .943 roughly.
02:01
The upper end is going to be 24 .857.
02:09
Then, for part b, we're asked to compute and interpret a 95 % prediction interval for the fat content of the next hot dog to be sampled from that population...