00:02
For part a, to construct a confidence interval for the mean weight of all college students, we use the formula for a confidence interval for the population when the sample size is relatively large at greater than 30 and the population standard deviation is not known.
00:16
So that confidence interval is the sample mean plus or minus the critical z times the standard deviation over the spread of the sample size.
00:23
Where in this case, the sample mean is 140 pounds, the critical z at 90 percent is 1 .645, the sample standard deviation is 26, and the sample size is 53.
00:38
Now the lower bound to this then would be found by subtracting 140 minus 1 .645 times 26 over the square root of 53, which is 134 .13 to three places, and the upper boundary found by adding 145 .87 to two places.
01:11
For part b, does the result mean that 90 percent of those students ' weight is in this range? no, it does not mean that.
01:21
Um, the confidence interval provides a range within which we are 90 percent confident the true population mean, um, in this case weight, lies.
01:32
But it doesn't imply that the individual student weights are distributed within that range...