Question

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.5 Suppose that the researchers test the hypotheses $H0:{\beta }_1=0$ versus

$Ha:{\beta }_1<0$. Which of the following is the value of the t statistic for this

test?

a. 2.61

b. −2.44

c. 2.44

d. −20.24

e. 0.081

Short answer

The correct answer is option (b) $-2.44$.

Step-by-step solution

Given information

To determine the value of the $t$ statistic from the given options.

Explanation

For shooting low scores and hence winning money, it is assumed that good putting is more significant than long driving. A random sample of players is picked for study to see if this is the fact.
They assumed that the slope inference conditions were met, and that the data was calculated using the computer output provided in the question.
Assume the researcher is putting the theory to the test.
$b=-4139198$
$S{E}_{b_1}=1698371$
$H_0:\beta =0$
$H_1:\beta <0$

Calculate the value of test statistics as follows:

$t=\frac{b-{\beta }_0}{S{E}_{b1}}$

$=\frac{-4139198-0}{1698371}$

$\approx -2.44$

As a result, the option (b)$-2.44$is the correct answer.