Homework

In case you were wondering...
According to an email I got from Prof Selcuk, there is no homework due this week. Homework #5 will be assigned this Thursday Feb 28 and due next Thursday March 6. It will be the last homework of the quarter.

My comment: This will give us time to absorb the material on linear regression before working on homework exercises. Maybe even time to go to the zoo on Sunday instead of doing homework.

Homework #4

It's kind of last minute, but... Exercises for Homework #4, due tomorrow, are:
8.19
8.21 a
8.43
8.65 a and c
9.31
9.45
9.59 a

In bothers me a bit that in the hypothesis testing that we're asked to do in the chapter 9 exercises, the sample means seem to fall either significantly outside the non-rejection region or clearly within the non-rejection region. You would think that these problems would involve more borderline cases where the you couldn't just solve the problem by inspection.

Case in point: One problem has a sample that has a std dev of around 25 and the sample mean is only about 1.5 less than the H₀ mean and we're asked to assess H₀ at a 0.05 level of significance. Isn't it obvious?

Homework #3

In case you didn't get it, the homework problems are:
6.11
6.35 a, b, c, d
7.55 a, b, c, d, e, f
8.7
8.9

Be careful with the parts of 8.7 that ask you to interpret the results of your calculations. Of course, be careful with all the other problems too.

Quartiles in HW1

Recall from a previous post that different software packages have different ways of calculating quartiles.

The formula for quartiles that we learned in class is:
Position of Q1 = (n+1)/4
Position of Q2 = (n+1)/2
Position of Q3 = 3(n+1)/4

Example: Let's say your data set is (2, 4, 6, 8, 10, 12, 14, 16)
n = 8
Position of Q1 = 9/4 = 2.25
We interpolate between the 2nd value (4) and the 3rd value (6) and get Q1 = 4.5

I haven't checked the documentation, but I've empirically determined that Minitab uses this same formula.

[EDIT] Before I go on to talk about Excel, I need to mention that the last step of interpolating between values is NOT how our book instructs us to calculate the quartile. Jeffrey McNamara pointed out to me that Rule 3 on page 77 says:

If the result is neither a whole number nor a fractional half, you round the result to the nearest integer and select that ranked value.

So in our example, where the position of Q1 is 2.25, we would round that to 2 and select the 2nd ranked value which is 4.

Again, Minitab uses the interpolation method and, as Frank Cardulla used to say, "You pays your money, you takes your choice."

Kudos to Jeff for the catch!
[/EDIT]

Excel uses a different formula which is apparently:
Position of Q1 = (n+3)/4

In our example, this would mean:
Position of Q1 = 11/4 = 2.75
Interpolating .75 between the 2nd and 3rd value gives us Q1 = 5.5

This is indeed what MS Excel calculated when I used the Quartile function on this data set.

Conclusion: It seems to me to be a good idea to use [either the book method or] Minitab (or manual calculations) to calculate the quartiles for the homework.

Homework 1 has been assigned

In case you didn't get it, homework #1 (due next Thursday) consists of the following exercises from the book:
1) 3.27 a, b and c
2) 3.35
3) 3.43
4) 3.61
5) 3.69
6) 4.11
7) 4.15

While we must maintain strict academic integrity, questions on the homework can be posted to comments. I'm moderating comments and I won't let anything through that would be questionable.

That said, I don't think there's any issue of integrity in explaining how to use Minitab or Excel to calculate the statistics, which may be a sticky point for first-time users. After all, it's a class in statistics, not in how to use the tools, right? Feel free to email me directly also.