Determine the regression equation.
| Question 1 | |||||||||||||||||
| A sample of 36 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level: | |||||||||||||||||
| H0: μ = 50 | |||||||||||||||||
| H1: μ ≠ 50 | |||||||||||||||||
| a. Is this a one- or two-tailed test? | |||||||||||||||||
| b. What is the decision rule? | |||||||||||||||||
| c. What is the value of the test statistic? | |||||||||||||||||
| d. What is your decision regarding H0? | |||||||||||||||||
| e. What is the p-value? |
| Question 2 | /4 | |||||||||||||||
| A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level: | ||||||||||||||||
| H0: μ ≤ 10 | ||||||||||||||||
| H1: μ > 10 | ||||||||||||||||
| a. Is this a one- or two-tailed test? | ||||||||||||||||
| b. What is the value of the test statistic? | ||||||||||||||||
| c. If the decision rule is to reject Ho when z > 2.33, what is your decision regarding H0? |
| Question 3 | /8 | |||||||||||||
| A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the 0.08 significance level: | ||||||||||||||
| H0: μ1 – μ2 ≤ 0 | ||||||||||||||
| H1: μ1 – μ2 > 0 | ||||||||||||||
| a. This is a one-tailed or a two-tailed test? | ||||||||||||||
| b. State the decision rule. (Hint: reject H0 if z is “greater than”/”less than” x…) | ||||||||||||||
| c. Compute the value of the test statistic. | ||||||||||||||
| d. What is your decision regarding H0? | ||||||||||||||
| e. What is the p-value? |
| Question 4 | /6 | ||||
| The following sample observations were randomly selected: | |||||
| X: | 4 | 5 | 3 | 6 | 10 |
| Y: | 4 | 6 | 5 | 7 | 7 |
| a. Determine the regression equation. | |||||
| b. Determine the value of Y’ when X is 7 |
| Question 5 | /8 | ||||||||||||||||
| The owner of Maumee Motors wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at Maumee Motors last year: | |||||||||||||||||
| Car | Age (years) | Selling Price ($ thousands) | |||||||||||||||
| 1 | 9 | 8.1 | |||||||||||||||
| 2 | 7 | 6 | |||||||||||||||
| 3 | 11 | 3.6 | |||||||||||||||
| 4 | 12 | 4 | |||||||||||||||
| 5 | 8 | 5 | |||||||||||||||
| 6 | 7 | 10 | |||||||||||||||
| 7 | 8 | 7.6 | |||||||||||||||
| 8 | 11 | 8 | |||||||||||||||
| 9 | 10 | 8 | |||||||||||||||
| 10 | 12 | 6 | |||||||||||||||
| 11 | 6 | 8.6 | |||||||||||||||
| 12 | 6 | 8 | |||||||||||||||
| a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable, and which is the independent variable? | |||||||||||||||||
| b. Determine the regression equation. | |||||||||||||||||
| c. Estimate the selling price of a 10-year-old car. |
