Chapter 5.2, Problem 5.54E

To determine

To stimulate the results of fifty samples by counting the number of $0\text{s and 1s}$ in the first $25$ entries in each of the fifty rows of Table B and then make histogram to display the result and then explain that is the truth about the population near the center of your graph or not and what are the largest and the smallest counts of the unemployed students we obtained in our fifty sample and what percent of our sample had either $4,5,\text{or 6}$ unemployed.

Answer to Problem 5.54E

Yes it is.

The smallest count is $\text{1}$ .

The largest count is $\text{9}$

Percent of sample is $66\%$

Explanation of Solution

  $\begin{array}{l}\text{The digits 0 and 1 represent unemployes students}\text{. we count the number of 0s and 1s}\\ \text{of the first 25 entries in each rows of table B}\text{. The resulting count will then }\\ \text{represent the number of unemployed students in a sample of size 25}\text{.}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 8 Unemployed}\\ \text{Row 101: 6 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 6 Unemployed}\\ \text{Row 101: 6 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 1 Unemployed}\\ \text{Row 101: 6 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 7 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 4 Unemployed}\\ \text{Row 101: 7 Unemployed}\\ \text{Row 101: 4 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 5 Unemployed}\\ \text{Row 101: 3 Unemployed}\\ \text{Similarly, the rsult for the remaining 30 rows are:}\\ \text{5,5,6,7,4,4,4,5,2,6,9,2,8,5,6,2,5,5,5,6,3,3,2,4,5,6,3,7,3,6}\end{array}$

The histogram is as follows:

  $\begin{array}{l}\text{We note that the highest bar in the histogram is at 5, thus the center of the distribution}\\ \text{is 5 and this corresponds with an unemployment rate of 20\%}\text{.}\\ \text{The samllest count was 1 unemployed, while the highest count was 9 unemployed}\text{.}\\ \text{6+17+10=30 of the 50 samples had a count of 4,5 or 6}\text{.}\\ \frac{33}{50}\\ =0.66\\ =66\%\\ \text{Thus 66\% of the sample had a count of 4,5 or 6 unemployed}\text{.}\end{array}$