Platinum Billiards, Inc., is a retailer of billiard supplies based in Jacksonville, Florida. It stands out among billiard suppliers because of the research it does to assure its products are top notch. One experiment was conducted to measure the speed attained by a cue ball struck by various weighted pool cues. The conjecture is that a light cue generates faster speeds while breaking the balls at the beginning of a game of pool. Anecdotal experience has indicated that a billiard cue weighing less than 19 ounces generates faster speeds. Platinum used a robotic arm to investigate this claim. Its research generated the data given in the file titled Breakcue.
a. To determine if there is a negative relationship between the weight of the pool cue and the speed attained by the cue ball, calculate a correlation coefficient.
b. Conduct a test of hypothesis to determine if there is a negative relationship between the weight of the pool cue and the speed attained by the cue ball. Use a significance level of 0.025 and a p -value approach.