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Spring 2003 Questions and Answers

Dr Short,
I was writing in regards to our homework assignment for monday. I followed the steps in the book for constructing a histogram on my calculator, but when i went to see the graph, nothing was there. I did have problems though understanding step 3 and the windows. It said to adjust the settings, but i wasn't sure what that meant, or how to do that. I wasn't sure what the titles Ymin and so on stood for.
Thats the only reason i can figure for the graph not turning out. If you could just drop me a quick line on what those settings meant, and how i can change them, i would greatly appreciate it. Thanks!

Hi Rebecca,

Thank you for sending your question.

The settings include Xmin, Xmax, Ymin, and Ymax.

Xmin and Xmax are the smallest and largest values on the horizontal or x-axis, and Ymin and Ymax are the smallest and largest values on the vertical, or y-axis.

For exercise 2.46, you might want to try values like these:

Xmin = 80 or so
Xmax = 120 or so (because these are about the smallest and largest values for the gasoline prices)

and maybe

Ymin = 0
Ymax = 5 or 10 or something (because this will be the count of how many observations fall in each bar)

Please let me know if you have any other questions.

Statistically yours,

Tom Short
tshort@iup.edu

Professor Short,

Could you explain to me how I can find a z-score and what significance it has? In problem 2.95 part c, it asks for z-scores, and I read the section in the book about z-scores, but I am still a bit confused.

Thank you for your time,
Rebecca

Hi Rebecca,

Thanks for the message, and thanks for trying the optional problems!

A z-score has a formula that looks like this:

z = (value - mean)/standard deviation.

So if the problem tells you that the mean and standard deviation are, then you can just plug them into the formula.

I guess the problem in part c is that you are not given the standard deviation - you have to calculate it and we haven't done that yet (we're going to do it tomorrow in class). So I will do it for you now.

I computed the mean of the down times to be 20.4 hours, and the standard deviation is 13.9 hours. You can use these figures to compute the z-scores in part (c) if you want.

I hope that someone will ask about this part in class tomorrow because it will help me to introduce standard deviations and z-scores.

Please let me know if you have any other questions.

Statistically yours,

Tom Short
tshort@iup.edu

Dr. Short,
I had a few quick questions on the homework. On question 2(a) it says to compute the 5 number summary. I am not sure how to do that and i couldn't find it in the book. If you could just give me a brief of how to do it, or tell me where it is in the book, that would really help.

My next question had to due with problem 3, the very last sentence about predicting how much a beanie baby goes up in value from current to retired. I am not sure how to go about solving this one. Any suggestions would be appreciated.

Thanks, Rebecca

Hi Rebecca,

Thanks for sending your questions.

A five number summary consists of the following values:

Minimum
Lower quartile
Median
Upper quartile
Maximum

These are the five numbers that go into making a boxplot. I don't have my textbook with me right now, so I can't give you a page reference. But look for boxplots and you should find the right information.

When you do problem 3, you should find a difference in the mean or median values for beanie babies that are current and those that are retired. If the mean difference is, say, $5.00, then you could predict that the value of a beanie babie increases by about $5.00 when it retires.

I hope these answers help. Please let me know if you have any other questions.

Statistically yours,

Tom Short
tshort@iup.edu

Hi Professor Short,

I am stuck on the very last problem of the review packet (#5) that you handed out to us that is due Wednesday. I am not sure I know how to find probability here. I don't know where to start. Do you think you could tell me how to get started with this problem?

Thanks!
Rebecca

Hi Rebecca,

Problem 5 in the packet is a normal distribution problem, so you should use the programs NORMAREA and NORMINV on your calculator to solve it.

Please let me know if you have any other questions.

Statistically yours,

Tom Short
tshort@iup.edu

Professor Short,
Could you explain how I solve problems 7.1 and 7.2? I see that there is a table on the previous page providing some of the answers, but I was wondering if there was a specific way to solve these problems instead of just looking at the chart.

Thanks,
Rebecca

Hi Rebecca,

Thank you for sending your question.

The short answer is that you can use the program NORMINV to help solve Exercise 7.1, and you can use NORMAREA to help with 7.2.

In Exercise 7.1 the area, which is called alpha, is the total area in both ends of a bell shaped curve. For example, in part (a), when alpha = 0.10, that means that there is 0.05 in each end and 0.90 in the middle. So you could use NORMINV and put in 0.95 for the area, 0 for the mean, and 1 for the standard deviation to find the thing the book calls z(alpha/2).

In Exercise 7.2 you know the cutoff. In part (a) the number is 1.96. So you can put -1.96 and 1.96 into program NORMAREA, with mean 0 and standard deviation 1. The answer you get will be the confidence level.

I'm sure that I will go over some of these problems tomorrow in class.

Please let me know if you have any other questions.

Statistically yours,

Tom Short
tshort@iup.edu