Connect hosted by ALEKS for Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781260041774
Author: Allan Bluman
Publisher: Mcgraw-hill Higher Education (us)
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Chapter 10, Problem 20CQ
a.
To determine
To construct: The
a.
Expert Solution
Answer to Problem 20CQ
Output using the MINITAB software is given below:
Explanation of Solution
Given info:
The data shows the age of a child (x) and the number of cavities (y) values.
Calculation:
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 ofNo.of cavities.
- Under X variables, enter a column ofAge of child.
- Click OK.
b.
To determine
To compute: The value of the
b.
Expert Solution
Answer to Problem 20CQ
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 x and y from the box on the left.
- Click OK.
Output using the MINITAB software is given below:
From the MINITAB output, the value of the correlation is 0.842.
c.
To determine
To test: The significance of the correlation coefficient at
c.
Expert Solution
Answer to Problem 20CQ
The conclusion is that,there is a linear relation between the age of a child and the number of cavities.
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 betweenthe age of a child and the number of cavities.
Alternative hypothesis:
That is, there is a linear relation between the age of a child and the number of cavities.
The sample size is 6.
The formula to find the degrees of the freedom is
That is,
From the “TABLE –I: Critical Values for the PPMC”, the critical value for 4 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 r is0.842that is the absolute value of r is 0.842.
Here, the absolute value of r is greater than the critical value
That is,
By the rejection rule,reject the null hypothesis.
There is asufficient evidence to support the claim that “there is alinear relation betweenthe age of a child and the number of cavities”.
d.
To determine
To find: The regression equation for the given data.
d.
Expert Solution
Answer to Problem 20CQ
The regression equation for the given datais
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 ofNo.of cavities.
- In Predictors, enter the column ofAge of child.
- Click OK.
Output using the MINITAB software is given below:
Thus, regression equation for the given datais
e.
To determine
To construct: The scatterplot for the variablesthe age of a child and the number of cavitieswith regression line.
e.
Expert Solution
Answer to Problem 20CQ
Output using the MINITAB software is given below:
Explanation of Solution
Calculation:
Step by step procedure to obtain scatterplot using the MINITAB software:
- Choose Graph > Scatterplot.
- Choose with line and then click OK.
- Under Y variables, enter a column of No.of cavities.
- Under X variables, enter a column ofAge of child.
- Click OK.
f.
To determine
To obtain: The predicted value of the number of cavities for a child of 11.
f.
Expert Solution
Answer to Problem 20CQ
Thepredicted value of the number of cavities is 4.143.
Explanation of Solution
Calculation:
Thus, regression equation for the given datais
Substitute x as 11 in the regression equation
Thus, the predicted value of the number of cavities is 4.143.
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Chapter 10 Solutions
Connect hosted by ALEKS for Elementary Statistics: A Step By Step Approach
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