How do we decide that we include -infinity in one sided interval or +infinity (a

Question

How do we decide that we include -infinity in one sided interval or +infinity (as done for the following question at the end of the solution):

dataset DS 9.2.6 used:

whatever data is used in this question is not necessary as important details of data are given in answer (given in link)

Full answer to this question is given on https://www.chegg.com/homework-help/golf-ball-designa-sports-manufacturer-developed-new-golf-bal-chapter-9.2-problem-6p-solution-9781133712763-exc

It is textbook question from Probability And Statistics for Engineers And Scientists, 4th Edition, chapter 9.2, problem 6p

Question: Golf Ball Design A sports manufacturer has developed a new golf ball with special dimples that it hopes will cause the ball to travel farther than standard golf balls. This question is examined by asking 24 golfers to hit ten new balls and ten standard balls. Each ball is hit off a tee, and randomization techniques are employed to account for any fatigue or wind effects. The distances traveled by the balls are measured, and DS 9.2.6 presents the average distances in yards for the ten shots for each of the 24 golfers and the two types of ball. What should the company conclude from this experiment? Why was it a good idea to use a paired design for this experiment?

Explanation / Answer

The inclusion of -infinity (OR +infinity) in any one sided confidence interval is a matter of theretical fact this has no practical importance as the probability that any value appears below(OR above) a very small(ORvery high) is negligible .But this ensures the theoretical interest of attaining exact confidence (here it is 95% ) .

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