00:01
So we're given test scores of 20 students on a 100 -point test, and we want to calculate the mean of the sample, which is the sum over all x's divided by the sample size n, and our sample is 20.
00:27
So this is x bar, and that is equal to 76 .7, and our standard deviation is going to be the square root of the variance, and the variance is the sum over all x of x minus x bar squared, and since this is a sample, we're dividing by n minus 1, and this then turns out to be 10 .332 if we want three decimal places.
01:17
So this is our standard deviation s, and then if these students give me considered a random sample from a normal population, then calculate a 95 percent confidence interval for the average test score in the population.
01:43
So for the mean, this is going to be x bar plus or minus t alpha over 2 is 0 .025.
01:54
We have n minus 1 or 19 degrees of freedom, and then we multiply that by s over the square root of n.
02:03
So this is going to be 76 .7 plus or minus the t value.
02:10
We look up in t table, and we have, let's see here, 19 degrees of freedom, 95 percent, so that is 2 .093, i believe...