00:01
For this exercise, we have a random sample of size 6, which was drawn from a normal distribution.
00:09
And given the sample data, we are asked to find a 95 % confidence interval for the population mean.
00:18
The formula for the confidence interval for the mean is the sample mean plus or minus critical value, t sub alpha over 2, with n minus 1 degrees of freedom, times the sample standard deviation.
00:35
Over the square root of the sample size.
00:39
So three pieces of information we need are the sample mean, the sample standard deviation, and this critical value.
00:46
So first for the sample mean and sample standard deviation, i'm going to calculate these in excel, so i have the data set or the sample entered in column a.
00:57
To find the mean, we can use the average function.
01:00
We start with an equal sign, type average, select that function, and then as the arguments we enter the the data points, or the sample points, hit enter, and we get a mean of six.
01:14
For the sample standard deviation, the function is std -ev .s.
01:22
And again, as the arguments we enter the sample data, and we get about 1 .789.
01:33
So we have a sample mean of six, sample standard deviation of 1 .7889.
01:43
Now, since we want a 95 % confidence interval, alpha is 1 minus .95, which is .05...