Chapter 5.3, Problem 5.68E

(a)

To determine

To explain how we would assign labels and use random digits to choose the desired result.

Answer to Problem 5.68E

  $\text{the female 138,158,52,87,359 are selected}\text{.}$

  $\text{Thus the first five male are: 1369,0815,0727,1025,1868}\text{.}$

Explanation of Solution

FEMALES:

  $\begin{array}{l}\text{We will first randomly assign an integer between 1 and 500 to each female,}\\ \text{according to their rank in the alphabetized list}\text{.}\\ \text{Select the first 3-digit number in the line 122 of table B}\text{.}\\ \text{If the number is between 001 and 500(including), then the corresponding}\\ \text{female is selected, else we ignore the number and select the next 3-digit number}\text{.}\\ \text{138=select female}\\ \text{738=Ignore}\\ \text{159=Select female}\\ \text{895=Ignore}\\ \text{052=Select female}\\ \text{909=Ignore}\\ \text{087=Select female}\\ \text{359=Select female}\\ \text{Thus the female 138,158,52,87,359 are selected}\text{.}\end{array}$

MALES:

  $\begin{array}{l}\text{We will first randomly assign an integer between 1 and 500 to each male,}\\ \text{according to their rank in the alphabetized list}\text{.}\\ \text{Select the first 4-digit number in table B}\text{.}\\ \text{If the number is between 0001 and 2000(including), then the corresponding}\\ \text{male is selected, else we ignore the number and select the next 4-digit number}\text{.}\\ \text{Thus the first five male are: 1369,0815,0727,1025,1868}\text{.}\end{array}$

(b)

To determine

To find out what is the chance that any one of the $2000$ males will be in the sample and also find out what is the chance that any one of the $500$ females will be in the sample

Answer to Problem 5.68E

For males: $\frac{1}{400}$ .

For females: $\frac{1}{100}$ .

Explanation of Solution

For Males:

  $\text{The 5 males were randomly selected from the 2000 males}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}\text{P(males)=}\frac{5}{2000}\\ =\frac{1}{400}\end{array}$

For Females:

  $\text{The 5 females were randomly selected from the 500 females}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}\text{P(females)=}\frac{5}{500}\\ =\frac{1}{100}\end{array}$

(c)

To determine

To explain why the conclusion give in the question is wrong.

Explanation of Solution

The conclusion does not take into account the different opinions of males and females, while the opinions for females and males appear to differ a lot.

To determine

(d)

To find out what is the chance and explain why this sample is not SRS.

Answer to Problem 5.68E

For males and females: $\frac{1}{10}$ .

Explanation of Solution

For Males:

  $\text{The 200 males were randomly selected from the 2000 males}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}\text{P(males)=}\frac{200}{2000}\\ =\frac{1}{10}\end{array}$

For Females:

  $\text{The 50 females were randomly selected from the 500 females}\text{.}$

The probability is the number of favorable outcomes divided by the number of possible outcomes:

  $\begin{array}{l}\text{P(females)=}\frac{50}{500}\\ =\frac{1}{10}\end{array}$

The systematic random sample is not a simple random sample because there are samples that cannot be selected, while there are samples that can be selected and thus all samples are not equally likely to be selected.