Chapter 2.2, Problem 36E

(a)

To determine

To find: A new data set that has Internet users as users per 10,000 people and births as births per 10,000 people.

Answer to Problem 36E

Solution: The partial data set is shown below:

Country Name	Country Code	Birth rate	Users Per 100	Users per 10000	Birth per 10000
Aruba	ABW	11.323	57.0684	5706.84	113.23
Angola	AGO	40.838	14.776	1477.6	408.38
Albania	ALB	12.748	49.00	4900	127.48
United Arab Emirates	ARE	12.755	70.00	7000	127.55
Argentina	ARG	17.006	47.7040	4770.4	170.06
Burundi	BDI	33.722	1.11	111	337.22
Benin	BEN	39.073	3.50	350	390.73

Explanation of Solution

Given: The data of birthrate (births per 1000 people) versus Internet use (users per 100 people) for 106 countries is given below.

Calculation: To obtain a new data set that has Internet users as users per 10,000 people and births as births per 10,000 people use Minitab. Follow the steps below:

Step 1: Open the Minitab worksheet which contains the data.

Step 2: Go to Calc > Calculator.

Step 3: Write “Users per 10000” in the column for Store result in variable. Select Users in the column for Expression and select “&*#8221; from the calculator and write $\left(10000/100\right)$ in the column for Expression.

Step 4: Click OK.

The new data set for users for 10,000 people is obtained. To obtain the new data set for Birthrate 2011 for 10,000 people follow the similar steps.

Step 1: Open the Minitab worksheet which contains the data.

Step 2: Go to Calc > Calculator.

Step 3: Write “Birth rate per 10000”in the column for Store result in variable. Select Birthrate 2011 in the column for Expression and select “&*#8221; from the calculator and write $\left(10000/1000\right)$ in the column for Expression.

Step 4: Click OK.

The new data set for Birthrate 2011 for 10,000 people is obtained. The partial data set is shown below:

Country Name	Country Code	Birth rate	Users	Users per 10000	Birth per 10000
Aruba	ABW	11.323	57.0684	5706.84	113.23
Angola	AGO	40.838	14.7760	1477.60	408.38
Albania	ALB	12.748	49.0000	4900.00	127.48
United Arab Emirates	ARE	12.755	70.0000	7000.00	127.55
Argentina	ARG	17.006	47.7040	4770.40	170.06
Burundi	BDI	33.722	1.1100	111.00	337.22
Benin	BEN	39.073	3.5000	350.00	390.73

(b)

To determine

To explain: The reason for these transformations to be linear transformations.

Answer to Problem 36E

Solution: These transformations are linear transformations because every variable is multiplied by a numerical value.

Explanation of Solution

Consider the results of part (a). The transformations provide the linearity for the new variables. These transformations can be considered as a linear transformations because every variable is multiplied by a number.

(c)

To determine

To graph: A scatterplot by using transformed variables.

Explanation of Solution

Graph: To obtain the scatterplot use Minitab. Follow the steps below:

Step 1: Go to Stat > Graph > Scatterplot > Simple.

Step 2: Select “Birth per 10,000” in Y variables and “Users per 10,000” in X variables.

Step 3: Click OK.

The required scatterplot is obtained as:

Interpretation: The scatterplot represents that the relationship between numbers of births per10,000 versus Internet users per 10,000 is negative.

(d)

To determine

To explain: The comparison between obtained scatterplot and figure 2.13.

Answer to Problem 36E

Solution: The obtained scatterplot in part (c) represents that the relationship between variables is more linear than the relationship which is represented by the scatterplot of births per 1000 people and internet users per 100 people. Both the scatterplots shows moderate relationship between the variables.

Explanation of Solution

The scatterplot which is obtained in part (c) represents that the relationship between numbers of births per 10,000 versus Internet users per 10,000 is negative.

The scatterplot of births per 1000 people and internet users per 100 people is shown below:

The scatterplot represents that the relationship between births per 1000 people versus Internet users per 100 people for 106 countries is quite linear and negative. The scatterplot which is obtained in part (c) represents that the relationship between birth rate per 10000 people and internet users per 10000 people is more linear than the provided scatterplot. Both the scatterplot show a moderate relationship between the variables.

(e)

To determine

To explain: The reason why World Bank selected Internet users as users per 100 people and births as births per 1000 people.

Answer to Problem 36E

Solution: To make the proper ratio, the analyst of World Bank selected Internet users as users per 100 people and births as births per 1000 people.

Explanation of Solution

The users of internet can be male or woman both but births can be given by females only. To make the ratio accurate, the analyst of World Bank selected Internet users as users per 100 people and births as births per 1000 people.