(Solved): Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tour ...

Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table. inal round cause scores to go up? Or does the increased player concentration cause scores to come down? (a) Use $$?=0.10$$ to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use $${?}_{\mathrm{d}}=$$ mean score first round $$?$$ mean score fourth round.) Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the $$p$$-value. (Round your answer to four decimal places.) $$p$$-value $$=$$ State your conclusion. round. round. (b) What is the point estimate of the difference between the two population means? (Use mean score first round - mean score fourth round.) $$x$$ For which round is the population mean score lower? The mean of the first round scores was lower than the mean of the fourth round scores. The mean of the fourth round scores was lower than the mean of the first round scores. (c) What is the margin of error for a $$90\%$$ confidence interval estimate for the difference between the population means? (Round your answer to two decimal Could this confidence interval have been used to test the hypothesis in part (a)? Explain. Yes. One could check to see if the $$90\%$$ confidence interval includes a difference of zero. If the interval does not contain 0 , the difference is not statistically significant. Yes. One could check to see if the $$90\%$$ confidence interval includes a difference of zero. If the interval contains 0 , the difference is not statistically significant. Yes. One could check to see if the $$90\%$$ confidence interval includes a difference of 1 . If the interval does not contain 1 , the difference is not statistically significant. Yes. One could check to see if the $$90\%$$ confidence interval includes a difference of 1 . If the interval contains 1 , the difference is not statistically significant. No. One can not use a confidence interval to test hypothesis in part (a) because hypothesis tests and confidence intervals are two different things.