Q.2.159 Class Project: Random Digits. Th... [FREE SOLUTION]

Chapter 2: Q.2.159 (page 83)

Class Project: Random Digits. This exercise can be done individually or, better yet, as a class project.
a. Use a table of random numbers or a random-number generator to obtain 50 random integers between $0$ and $9$ .
b. Without graphing the distribution of the $50$ numbers you obtained, guess its specific shape. Explain your reasoning.
c. Construct a relative-frequency histogram based on single-value grouping for the $50$ numbers that you obtained in part (a). Is its shape about what you expected?
d. If your answer to part (c) was "no," provide an explanation.
e. What would you do to make getting a "yes" answer to part (c) more plausible?
f. If you are doing this exercise as a class project, repeat parts (a) -(c) for $10000$ random integers.

Short Answer

Expert verified

a. The 50 random variables are: $9, 0, 4, 8, 8, 9, 4, 5, 5, 0, 6, 9, 5, 4, 4, 6, 9, 5, 5, 0, 1, 3, 9, 6, 6 5, 3, 9, 5, 7, 0, 8, 7, 0, 4, 0, 6, 0, 4, 7, 7, 7, 7, 2, 7, 8, 8, 7, 1, 1$

b. The shape of the distribution will be uniform.

c. The relative frequency histogram will be:

d. A source of sample variability always exists, causing the sample distribution to differ from the population distribution.

e. The answer is yes if the sample size was large enough to represent the entire population.

Step by step solution

Part (a) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (a) Step 2: Explanation

The 50 numbers will be generated using a random variable table.

$9, 0, 4, 8, 8, 9, 4, 5, 5, 0, 6, 9, 5, 4, 4, 6, 9, 5, 5, 0, 1, 3, 9, 6, 6 5, 3, 9, 5, 7, 0, 8, 7, 0, 4, 0, 6, 0, 4, 7, 7, 7, 7, 2, 7, 8, 8, 7, 1, 1$

Part (b) Step 1: Concept introduction

Part (b) Step 2: Explanation

The distribution should be uniform because each digit is equally likely to occur, hence each digit should appear the same amount of times.

Part (c) Step 1: Concept introduction

Part (c) Step 2: Explanation

The frequency distribution is

The relative frequency histogram is:

Part (d) Step 1: Concept introduction

Part (d) Step 2: Explanation

Because the sample only reflects a portion of the population, we anticipate the sample distribution to be similar to the population distribution. A source of sample variability always exists, causing the sample distribution to differ from the population distribution.