
Concept explainers
(a)
To test: The verification of
(a)

Answer to Problem 7P
Solution: It is verified that,
Explanation of Solution
Calculation: Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season.
The following table shows the
67 | 44 | 4489 | 1936 | 2948 |
65 | 42 | 4225 | 1764 | 2730 |
75 | 48 | 5625 | 2304 | 3600 |
86 | 51 | 7396 | 2601 | 4386 |
73 | 44 | 5329 | 1936 | 3212 |
73 | 51 | 5329 | 2601 | 3723 |
439 | 280 | 32393 | 13142 | 20599 |
In above table, the last column shows the total of corresponding column.
So,
The correlation coefficient, r is calculated as follows:
Conclusion: Hence, it is verified that,
(b)
To test: The claim that
(b)

Answer to Problem 7P
Solution: We have sufficient evidence to conclude that the population
Explanation of Solution
Calculation: 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 abovetest is right tailed test, so we can use the one-tail area in the student’s distributiontable (Table 4 of the Appendix). From table, the
Conclusion: We have sufficient evidence to conclude that the population correlation coefficient between x and y is positive at 5% level of significance.
(c)
To test: The verification of
(c)

Answer to Problem 7P
Solution: It is verified that,
Explanation of Solution
Calculation: The results obtained in part (a) are,
Now,
Conclusion: Hence, it is verified that,
(d)
To find: The predicted percentage
(d)

Answer to Problem 7P
Solution: The predicted percentage
Explanation of Solution
Calculation: The results obtained in above part are
The regression line equation is
Now to find the predicted
Interpretation: The predicted percentage
(e)
To find: The 90% confidence interval for
(e)

Answer to Problem 7P
Solution: The 90% confidence interval for
Explanation of Solution
Calculation: The find 90% confidence interval for
Step 1: Go to Stat >Regression>Regression > Predict.
Step 2: Select ‘y’ in Response and write 70 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:
Interpretation: The 90% confidence interval for
(f)
To test: The claim that
(f)

Answer to Problem 7P
Solution: We have sufficient evidence to conclude that the slopeis positive at 5% level of significance.
Explanation of Solution
Calculation: 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 testwe can divide the obtained P-value by 2.
Since P-value is less than 0.05, hence we can reject the null hypothesis at
Conclusion: We have sufficient evidence to conclude that the slopeis positive at 5% level of significance.
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Chapter 11 Solutions
Understanding Basic Statistics
- ian income of $50,000. erty rate of 13. Using data from 50 workers, a researcher estimates Wage = Bo+B,Education + B₂Experience + B3Age+e, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. ni ogolloo bash 1 Standard Coefficients error t stat p-value Intercept 7.87 4.09 1.93 0.0603 Education 1.44 0.34 4.24 0.0001 Experience 0.45 0.14 3.16 0.0028 Age -0.01 0.08 -0.14 0.8920 a. Interpret the estimated coefficients for Education and Experience. b. Predict the hourly wage rate for a 30-year-old worker with four years of higher education and three years of experience.arrow_forward1. If a firm spends more on advertising, is it likely to increase sales? Data on annual sales (in $100,000s) and advertising expenditures (in $10,000s) were collected for 20 firms in order to estimate the model Sales = Po + B₁Advertising + ε. A portion of the regression results is shown in the accompanying table. Intercept Advertising Standard Coefficients Error t Stat p-value -7.42 1.46 -5.09 7.66E-05 0.42 0.05 8.70 7.26E-08 a. Interpret the estimated slope coefficient. b. What is the sample regression equation? C. Predict the sales for a firm that spends $500,000 annually on advertising.arrow_forwardCan you help me solve problem 38 with steps im stuck.arrow_forward
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- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
