This dataset contains scores in the first and fourth rounds for a samp This dataset contains scores in the first and fourth rounds for a sample of 20 golfers who competed in PGA tournaments in 2009. A sports fan suspects that scores in the first round are lower due to less pressure. You are to test whether this is true. 1. State the null and alternative hypotheses (take round 1 scores - round 4 scores). 2. Is this a lower tail, upper tail or two-tailed test? 3. Use Excel to carry out the test. Use a= 0.05. What is the value of the test statistic? 4. What is the p-value? 5. What is your conclusion using a = 0.05? 6. State your conclusion in words a non-statistician could understand.
Paper For Above instruction The aim of this study is to assess whether golfers' scores in the first round are statistically lower than their scores in the fourth round, possibly due to varying pressure levels. The hypothesis testing approach provides a structured method to analyze this question using paired sample data collected from 20 PGA golfers in 2009. Hypotheses Formulation In hypothesis testing, the null hypothesis (H■) typically assumes no effect or no difference, while the alternative hypothesis (H■) reflects the suspected effect. Here, since the claim is that scores in the first round are lower (which equates to lower numerical scores in golf), the hypotheses are formulated as: Null hypothesis (H■): The average difference between first and fourth round scores is zero or positive (no improvement or worse in the first round). Mathematically, H■: µ■ - µ■ ≥ 0. Alternative hypothesis (H■): The average first round scores are lower than the fourth round scores, implying scores decrease from the fourth to the first round. Mathematically, H■: µ■ - µ■ < 0. This is a left-tailed test, as we are testing whether the first round scores are significantly lower. Type of Test Since the data involve paired samples (each golfer has two scores: in the first and fourth rounds), and we are comparing the means of these differences, a paired t-test is appropriate. The specific alternative hypothesis indicates a lower tail test, focusing on whether the mean difference (round 1 minus round 4) is