Question

Birdies and Score. The data from Exercise 14.34 for number of birdies during a tournament and final score of 63 women golfers are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for women golfers, number of birdies and score are negatively linearly correlated?

Short answer

the data provide sufficient evidence to conclude that for women golfers number of birdies and score are negatively linearly correlated.

Step-by-step solution

Step 1:Given information

The data from Exercise 14.34 for number of birdies during a tournament and final score of 63 women golfers are on the WeissStats site.

Step 2:Explaination

Check whether reasonably to apply the correlation $t$-test procedure to data by using Exercise 14.34.

- From the residual plot, it is clear that the residuals are fall in the horizontal band.

- From the normal probability plot of residuals, it is clear that the residuals are in the linear pattern.

Hence, the assumptions for the regression inferences are not violated for the variables birdies and scores.

The test hypotheses are as follows:

Null hypothesis:

$H_0:\rho =0$

That is, the data does not provide sufficient evidence to conclude that for women golfers number of birdies and score are negatively linearly correlated.

Alternative hypothesis:

$H_a:\rho <0$

That is, the data provide sufficient evidence to conclude that for women golfers number of birdies and score are negatively linearly correlated.

Obtain the correlation and $p$-value between BIRDIES and SCORE by using MINITAB.

MINITAB procedure:

Step 1: SelectStat >Basic Statistics > Correlation.

Step 2: In Variables, select BIRDIES and SCOREfrom the box on the left.

Step 3: Click OK.

MINITAB output:

Conclusion:

Use the significance level, $\alpha =0.05$

Here, $p$-value is less than the level of significance.

That is, $p$-value $(=0.000)<\alpha (=0.05)$.

Therefore, by the rejection rule, it can be concluded that there is evidence to reject the null hypothesis $\left(H_0\right)$at $\alpha =0.05$.

That is, the data provide sufficient evidence to conclude that for women golfers number of birdies and score are negatively linearly correlated.