Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 32.4 32.9 36.1 44.0 47.8 y 30.4 31.0 32.0 42.1 42.2 (a) Verify that Σx = 193.2, Σy = 177.7, Σx2 = 7656.22, Σy2 = 6462.41, Σxy = 7029.62, and r ≈ 0.975. Σx ? Σy ? Σx2 ? Σy2 ? Σxy ? r ? (b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t ? critical t ? (c) Verify that Se ≈ 1.5629, a ≈ 2.5006, and b ≈ 0.8551. Se ? a ? b ? (d) Find the predicted dealer invoice when the list price is x = 42 (thousand dollars). (Use 2 decimal places.) (e) Find a 95% confidence interval for y when x = 42 (thousand dollars). (Use 2 decimal place.) lower limit ? upper limit ? (f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.) t ? critical t ? (g) Find a 95% confidence interval for β and interpret its meaning. (Use 3 decimal places.) lower limit ? upper limit ?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle.
| x | 32.4 | 32.9 | 36.1 | 44.0 | 47.8 |
| y | 30.4 | 31.0 | 32.0 | 42.1 | 42.2 |
(a) Verify that Σx = 193.2, Σy = 177.7, Σx2 = 7656.22, Σy2 = 6462.41, Σxy = 7029.62, and r ≈ 0.975.
| Σx | ? |
| Σy | ? |
| Σx2 | ? |
| Σy2 | ? |
| Σxy | ? |
| r | ? |
(b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.)
| t | ? |
| critical t | ? |
(c) Verify that Se ≈ 1.5629, a ≈ 2.5006, and b ≈ 0.8551.
| Se | ? |
| a | ? |
| b | ? |
(d) Find the predicted dealer invoice when the list price is x = 42 (thousand dollars). (Use 2 decimal places.)
(e) Find a 95% confidence interval for y when x = 42 (thousand dollars). (Use 2 decimal place.)
| lower limit | ? |
| upper limit | ? |
(f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.)
| t | ? |
| critical t | ? |
(g) Find a 95% confidence interval for β and interpret its meaning. (Use 3 decimal places.)
| lower limit | ? |
| upper limit | ? |
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