SCCC 312A – ProSeminar in Statistics

Lecture Homework #5

Due Date: 2/6/04 (2/16/04)

Part I: Book Problems

On page 158 do 4.3, 4.6

On pages 161-162 do 4.12, 4.13

On pages 167-168 do 4.21, 4.25, 4.26

On pages 172-173 do 4.35, 4.38, 4.41

Part II: A Hands-On-Experience with “Order Out Of Chaos”

1. Repeat the following experiment 100 times (if you want you may do it more times, but no less than 100 times!) and record the number of "heads" that occur in each repetition. The experiment is to toss a nickel, a dime, and a quarter simultaneously. Write down the outcomes as a sequence of 100 numbers in the following table.

Sequence of Outcomes of Your Experiment

When you look at the sequence of outcomes you obtained in the table above, do you notice any patterns, or would you describe the sequence of outcomes as "chaotic"?

2. Determine the frequency in which you obtained 0 heads, 1 head, 2 heads, and 3 heads, and then compute the observed proportions, which are the frequencies divided by 100. Summarize your results in the following table.

Number of Heads	Observed Frequency	Observed Proportion	Theoretical Probability
0			.125
1			.375
2			.375
3			.125

Construct a relative frequency histogram of the results, that is, a histogram of "Number of Heads" versus "Observed Proportion." Describe the shape of the resulting histogram.

3. The values in the column labeled "Theoretical Probability" were computed using the binomial probability function (which will be studied later) and under the assumption that the coins are fair. Compare the observed proportions your obtained from your experiment with these theoretical probabilities. How would you describe the degree of agreement?

4. If you had repeated the experiment many more times, would you expect the observed proportions to be closer to the theoretical probabilities? Explain your answer.