(a)
To test: The verification of
(a)
Answer to Problem 14CR
Solution: It is verified that,
Explanation of Solution
Calculation: Let x be the body weight of a child (in kilograms), and let y be the metabolic rate of the child (in 100 kcal/24 h).
We have,
We have to calculate first
Conclusion: Hence, it is verified that,
(b)
To test: The verification of
(b)
Answer to Problem 14CR
Solution: It is verified that
Explanation of Solution
Calculation:
The correlation coefficient, r is calculated as follows:
Using the level of significance,
The null hypothesis for testing is defined as,
The alternative hypothesis is defined as,
The sample test statistic is,
The degrees of freedom are
The above test is right tailed test, so we can use the one-tail area in the student’s distribution table (Table 4 of the Appendix). From table, the p-value for the sample test statistic
Conclusion: It is verified that
(c)
To test: The verification of
(c)
Answer to Problem 14CR
Solution: It is verified that,
Explanation of Solution
Calculation:
The value b is calculated as follows:
Using the level of significance,
The null hypothesis for testing is defined as,
The alternative hypothesis is defined as,
The find t statistic and P-value using MINITAB software is as:
Step 1: Enter x and y in Minitab worksheet.
Step 2: Go to Stat > Regression > Regression > Fit Regression Model.
Step 2: Select ‘y’ in Response and ‘x’ in ‘Continuous predictors’ box. Then click on OK.
The sample test statistic is
The software gives the P-value for two-tailed test, for finding the p-value for one tailed test we can divide the obtained P-value by 2.
Since P-value is less than 0.01, hence we can reject the null hypothesis at
Conclusion: Hence, it is verified that,
(d)
To test: The verification of
(d)
Answer to Problem 14CR
Solution: It is verified that,
Explanation of Solution
Calculation: The results obtained in above part are
The regression line equation is
The find 90% confidence interval for
Step 1: Go to Stat > Regression > Regression > Predict.
Step 2: Select ‘y’ in Response and write 10 in ‘x’ box.
Step 3: Click on Options write 90 in ‘Confidence level’ and select ‘Two-sided’ in Type of interval. Then click on OK.
The 90% confidence interval is obtained as:
Conclusion: Hence, it is verified that,
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Chapter 11 Solutions
Understanding Basic Statistics
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