Chapter 5.2, Problem 5.37E

(a)

To determine

To draw twenty SRSs of size five using a different part of table B each time and then record the number of females in each of your samples.

Answer to Problem 5.37E

  $\begin{array}{l}\text{We then note that the number of female in each of the sample is:}\\ \text{1,1,2,2,2,3,0,1,2,2,3,2,1,2,2,1,1,2,3,2}\text{.}\end{array}$

Explanation of Solution

  $\begin{array}{l}\text{Let us rank the 25 individuals from 1 to 25:}\\ \text{Alonso=1}\\ \text{Binet=2}\\ \text{Blumenbach=3}\\ \text{Chase=4}\\ \text{Chen=5}\\ \text{Darwin=6}\\ \text{Epstein=7}\\ \text{Ferri=8}\\ \text{Gonzales=9}\\ \text{Gupta=10}\\ \text{Herrnstein=11}\\ \text{Jimenez=12}\\ \text{Lup=13}\\ \text{Moll=14}\\ \text{Morales=15}\\ \text{Myrdal=16}\\ \text{Perez=17}\\ \text{Spencer=18}\\ \text{Thomston=19}\\ \text{Taulmin=20}\\ \text{Vogt=21}\\ \text{Went=22}\\ \text{Wilson=23}\\ \text{Yerkes=24}\\ \text{Zimmer=25}\\ \text{Note that the females are 2,4,5,10,12,14,15,17,18,21}\text{.}\end{array}$

  $\begin{array}{l}\text{We will select 20 different rows}\text{. For each row, we select the first 2-digit number}\text{.}\\ \text{If the number is between 01 and 25, then the corresponding individual is}\\ \text{selected, else we ignore the number and select the next 2-digit number}\text{. We }\\ \text{repeat this until we obtained 5 unique individuals for the sample}\text{.}\\ \text{Row 101: 19,22,05,13,25}\\ \text{Row 102: 19,09,22,05,07}\\ \text{Row 103: 09,22,05,07,02}\\ \text{Row 104: 07,02,01,18,25}\\ \text{Row 105: 07,02,01,18,25}\\ \text{Row 106: 13,15,08,21,14}\\ \text{Row 107: 20,11,07,20,24}\\ \text{Row 108: 07,20,24,17,09}\\ \text{Row 109: 15,23,16,19,18}\\ \text{And so on to}\mathrm{..}\\ \text{Row 118: 19,03,25,04,02}\\ \text{Row 119: 18,20,16,04,21}\\ \text{Row 120: 16,04,21,19,07}\\ \text{We then note that the number of female in each of the sample is:}\\ \text{1,1,2,2,2,3,0,1,2,2,3,2,1,2,2,1,1,2,3,2}\text{.}\end{array}$

(b)

To determine

To construct a dot plot to display your results and find out what is the average number of females in your twenty sample.

Answer to Problem 5.37E

The average is

  $1.75$ .

Explanation of Solution

The dot plot of the data is as follows:

The average is the sum of all values divided by the number of values:

  $\begin{array}{l}\overline{x}=\frac{1+1+2+2+\mathrm{....}+1+2+3+2}{20}\\ =\frac{35}{20}\\ =1.75\end{array}$

(c)

To determine

To find out that do we think the club members should suspect discrimination if none of the five tickets goes to women and justify it.

Answer to Problem 5.37E

No.

Explanation of Solution

No we do not think the club members should suspect discrimination if none of the five tickets goes to women because in the twenty sample of part (a), we note that there was one sample with no women and thus the event of no women is likely to occur.