A coal of financial literacy for children is to learn how to...

A coal of financial literacy for children is to learn how to manage money wisely one question is how much money do children have to manage a recent study by Schnur educational research associates randomly sampled 15 children between eight and 10 years old and 16 children between 11 and 14 years old the test assumption that the population variances are equal using a 0.10 significant level

Transcript

00:01 We will be assuming that the mean allowance for the 8 to 10 year olds is equal to that of the 11 to 14 year old, and alternately that the 11 to 14 year old is higher.

00:16 And looking at the numbers, you know, probably is going to be higher, significantly higher.

00:21 All right.

00:22 Now, let's find what our samples give us, and we have a sample of, let's see.

00:30 We have a sample of 15 in this age group, so we have 15 in this age group, and that group had an x bar of 28 .8 with a sample standard deviation of 3 .16, and we'll call that 7.

00:50 And the other group, that was the 18, that were in 11 to 14 years old, they had a mean of, and then we go back up, 41 .2, so that looks to be higher.

01:05 And a sample standard deviation there of 4 .833.

01:09 Now we're going to pull those together.

01:10 I'm going to assume that these two standard deviations are equal, and so let's find what the pooled standard deviation is.

01:18 So here's the formula for the variance.

01:20 And we're going to take one less than the sample size times the variance of the first group.

01:25 And then one less than the sample size times the variance of the second group.

01:31 And then we will add the 15 and the 18 less two.

01:36 And so we end up getting that, the degrees of freedom.

01:40 Degrees of freedom here ends up being 31.

01:42 And i have what the standard deviation is.

01:45 I already have it square rooted.

01:47 And that comes out to be 4 .16.