Question

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 and the player’s total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypotheses $H_0:\beta =0$: $H_a:\beta <0$. The value of the t statistic for this test is

(a)$2.61$

(b)$2.44$

(c)$0.081$

(d)$-2.44$

(e) $-20.24$

Short answer

The value of the$t$ statistic for this test is option (d) $-2.44$

Step-by-step solution

Given information

Given in the question that, the 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 and the player’s total winnings for the previous season is recorded.

Explanation

The given values are

$b=-4139198$

$S{E}_b=1698371$

$H_0:\beta =0$

$H_a:\beta <0$

Find the value of test statistic

localid="1650644518754" $$\begin{gathered} t=\frac{b-{\beta }_0}{S{E}_b} \\ =\frac{-4139198-0}{1698371} \\ \approx -2.437 \\ \approx -2.44 \end{gathered}$$.