A Firm Is Experiencing Theft Problems at Its Warehouse -Which of the Following Is Correct at the 1% Level

question 32

Multiple Choice

A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent) . In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:
$$\begin{array} { c l l l l l } \text { DEPENDENT VARIAELE: } & \text { T } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ONF } \\\text { OESERVATIONS: } & 27 & \mathbf { 0 . 7 7 9 3 } & 42.38 & \mathbf { 0 . 0 0 0 1 } & \\& & \text { PARAMETER } & \text { STANDARD } & & \\\text { VARIAELE } & & \text { ESTMATE } & \text { ERROR } & \text { T-RATIO } & \text { P-VALUE } \\\text { INTERCEPT } & & 5150.43 & 1740.72 & \mathbf { 2 . 9 6 } & \mathbf { 0 . 0 0 6 8 } \\\text { G } & & - 480.92 & 130.65 & - \mathbf { 3 . 6 8 } & \mathbf { 0 . 0 0 1 2 } \\\text { U } & & 211.0 & 75.0 & \mathbf { 2 . 8 1 } & \mathbf { 0 . 0 0 9 5 }\end{array}$$
-Which of the following is correct at the 1% level of significance?

• A) The regression equation as a whole is statistically significant because the p-value of F is smaller than 0.01.
• B) The estimates of the parameters a, b, and c are all statistically significant because the absolute values of their t-ratios exceed 2.797.
• C) The estimates of the parameters a, b, and c are all statistically significant because the p- values for, \(\hat { a }\) ,\(\hat { b }\) and\(\hat { c }\) are all less than 0.01.
• D) The critical value of t is 2.797.
• E) all of the above

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