Elementary Statistics: A Step-by-Step Approach with Formula Card
9th Edition
ISBN: 9780078136337
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Question
Chapter 10, Problem 10.1.7RE
a.
To determine
To construct: The
a.
Expert Solution
Answer to Problem 10.1.7RE
The scatterplot for the data is as follows,
Explanation of Solution
Given info:
The data represents the numbers of male and female physicians.
Calculation:
Software procedure:
Step by step procedure to obtain scatterplot using the MINITAB software:
- Choose Graph > Scatterplot.
- Choose Simple and then click OK.
- Under Y variables, enter a column of Male.
- Under X variables, enter a column of Female.
- Click OK.
b.
To determine
To compute: The value of the
b.
Expert Solution
Answer to Problem 10.1.7RE
The value of the
Explanation of Solution
Calculation:
Correlation coefficient r:
Software Procedure:
Step-by-step procedure to obtain the ‘correlation coefficient’ using the MINITAB software:
- Select Stat >Basic Statistics > Correlation.
- In Variables, select Male and Female from the box on the left.
- Click OK.
Output using the MINITAB software is given below:
Thus, the value of the correlation is 0.907.
c.
To determine
To test: The significance of the correlation coefficient at
c.
Expert Solution
Answer to Problem 10.1.7RE
The conclusion is that, there is linear relation between the number of male and female physicians.
Explanation of Solution
Given info:
The level of significance is
Calculation:
The hypotheses are given below:
Null hypothesis:
That is, there is no linear relation between the number of male physicians and number of female physicians.
Alternative hypothesis:
That is, there is a linear relation between the number of male physicians and number of female physicians.
The formula to obtain the degrees of the freedom is
That is,
From the “TABLE –I: Critical Values for the PPMC”, the critical value for 5 degrees of freedom and
Rejection Rule:
If the absolute value of r is greater than the critical value then reject the null hypothesis.
Conclusion:
From part (b), the value of the correlation of Men and Women is 0.907. That is the absolute value of r is 0.907.
Here, the absolute value of r is greater than the critical value.
That is,
By the rejection rule, the null hypothesis is rejected.
Therefore, there is sufficient evidence to support the claim that “there is a linear relation between the number of male and female physicians”.
d.
To determine
To find: The regression equation for the given data
d.
Expert Solution
Answer to Problem 10.1.7RE
The regression equation for the given data is
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to obtain the regression equation using the MINITAB software:
- Choose Stat > Regression > Regression.
- In Responses, enter the column of Female.
- In Predictors, enter the column of Male.
- Click OK.
Output using the MINITAB software is given below:
Thus, the regression equation for the given data is
e.
To determine
To construct: The regression line on the scatter plot if appropriate.
e.
Expert Solution
Answer to Problem 10.1.7RE
The regression line on the scatter plot the scatterplot is as follows,
Explanation of Solution
Calculation:
Step by step procedure to obtain scatterplot using the MINITAB software:
- Choose Graph > Scatterplot.
- Choose With Regression and then click OK.
- Under Y variables, enter a column of Male.
- Under X variables, enter a column of Female.
- Click OK.
f.
To determine
To predict: The number of male specialists when there are 2,000 female specialists.
f.
Expert Solution
Answer to Problem 10.1.7RE
The predicted value of number of male specialists when there are 2,000 female specialists is 6,923.
Explanation of Solution
From part (d), the regression equation for the given data is
Substitute x as 2,000 in the regression equation
Thus, the predicted value of number of male specialists when there are 2,000 female specialists is 6,923.
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Chapter 10 Solutions
Elementary Statistics: A Step-by-Step Approach with Formula Card
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