A sporting goods manufacturing company wanted to compare the performance of four designs of golf balls in terms of the average distance travelled by...

A sporting goods manufacturing company wanted to compare the performance of four designs of golf balls in terms of the average distance travelled by balls. The company approached a professional golfer and gave him 10 balls of each design for testing. The pro was not told of the type of ball that was being hit. All 40 balls were hit in a short period of time so that the environmental conditions did not affect the performance of the balls. The distances travelled in metres by each ball are given in the table that follows.

(a) Name a statistical procedure that will facilitate the company make comparison of the four designs of golf balls. Using Excel, run this procedure on the given data.

(b) On the basis of average distance travelled by golf balls of each design, which design seems to be the best in producing balls with long drives? Explain your reason.

(c) Would you consider design 2 to be better than or at least comparable to design 1? Explain the reason for your choice of the design.

(d) Can we conclude at the 5% level of significance that there is a significant difference in the average distance travelled by balls of the four designs? Your answer must include the following:

(i) Appropriate null and alternative hypotheses

(ii) The value of the test statistic used and the distribution this test statistic follows

(iii) The decision rule based on the p‐value

(iv) Conclusion about the average performance of four designs of balls in terms of average distance travelled.

(e) If the answer in part (d) indicates the existence of significant differences in average distances travelled by the four types of balls, apply an appropriate test to determine which pairs of ball designs produce statistically different average distances. Use a 5% level of significance and show all details.