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An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� 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鈥檚 world money list are examined. The average number of putts per hole and the player鈥檚 total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

A $95\%$confidence interval for the slope $B$of the population regression line is

(a)$7,897,179卤3,023,782$

(b)$7,897,179卤6,047,564$

(c)$鈭�4,139,198卤1,698,371$

(d)$鈭�4,139,198卤3,328,807$

(e)$鈭�4,139,198卤3,396,742$

Step by step solution

01

Given information

Given in the question that

$$\begin{gathered} b=鈭�4139198 \\ S{E}_b=1698371 \\ n=69 \end{gathered}$$

02

Calculation

The confidence interval boundaries are

$b卤t脳S{E}_b$

The degree of freedom is

$$\begin{gathered} df=n鈭�2 \\ =69鈭�2 \\ =67>60 \end{gathered}$$

The critical t-value is shown in table in the row of $df=60$and column of $c=95\mathrm{\%}$

$t^{鈭�}=2.000$

The confidence interval boundaries become then :

$$\begin{gathered} b卤t^{鈭�}脳S{E}_b=鈭�4139198卤2.000脳1698371 \\ =鈭�4139198卤3396742 \end{gathered}$$

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