ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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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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Students have asked these similar questions
Reconsider the patient satisfaction data in Table 1. Fit a multiple regression model using both patient age and
severity as the regressors.
(a) Test for significance of regression.
(b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model?
(c) Has adding severity to the model improved the quality of the model fit? Explain your answer.
The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at
random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37,
10.44, 9.25, 9.38, and 10.85.
(a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a = 0.05.
(b) Construct a 95% two-sided confidence interval on μ.
(c) Test the hypothesis that σ² = 11 using α = 0.05.
(d) Construct a 95% two-sided confidence interval on σ.
(e) Construct a 95% upper confidence interval on σ.
(f) Does the assumption of normality seem reasonable for the output voltage?
Analyze the residuals from the regression model on the patient satisfaction data from Exercise 3. Comment on
the adequacy of the regression model.
Chapter 10 Solutions
ALEKS 360 ELEM STATISTICS
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Ch. 10.1 - When two variables are correlated, can the...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 23ECh. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - For Exercises 11 through 27, perform the following...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECCh. 10.1 - Prob. 29ECCh. 10.1 - Prob. 30ECCh. 10.2 - Applying the Concepts 102 Stopping Distances...Ch. 10.2 - What two things should be done before one performs...Ch. 10.2 - What are the assumptions for regression analysis?Ch. 10.2 - Prob. 3ECh. 10.2 - What is the symbol for the slope? 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