00:01
All right, so we're looking at a sample of 25 randomly selected college students, freshman college students, and we wanted to find a 95 % conference interval estimate for the average number of hours of all college freshmen spend watching tv in videos per week.
00:23
So we're given the sample size is 25.
00:26
The sample mean, which is the number of hours, is 14, and the sample standard deviation and s is 3 .2 hours.
00:35
And the formula for the confidence interval about the population mean is given as x bar plus minus t alpha over 2 noting the degrees of freedom times the sample standard deviation divided by the square root of the sample size.
00:56
So i have, we have to note the confidence interval here because this tells us the alpha, so it's a 95 % confidence interval.
01:12
So the alpha is the value that makes us 100%.
01:15
So in this case, the alpha is 0 .05.
01:20
So we can start substituting in what we have.
01:23
So x bar is 14 plus minus t .05 over 2.
01:30
And the degrees of freedom is given as n minus 1, so 25 minus 1, 24 times the sample.
01:41
Sample standard evasion of 3 .2 divided by the square root of 25.
01:48
So i've called this out se here.
01:56
This is the standard error.
01:57
It's, this should say s here, right there, sample standard evasion 3 .2.
02:07
Standard error is s over root n.
02:10
So 3 .2 divided by root 25 ends up being .64.
02:14
The t value, this is, found in like a textbook or i use my spreadsheet, but either way you'll get the same value.
02:25
The t value ends up being 2 .064.
02:32
But as you can see, i use my full spreadsheet precision here...