Do left handed starting pitchers pitch the same number of innings per game on average as right handed starting pitchers? A researcher looked at nine randomly selected left handed starting pitchers' games and eleven randomly selected right handed pitchers games. The table below shows the results. Left: 7 4 7 5 5 Right: 5 5 6 6 5 6 5 Assume that both populations follow a normal distribution. What can be concluded at the the or = 0.10 level of significance level of significance? For this study, we should use t-test for the difference between two independent population means V a. The null and alternative hypotheses would be: Ho: w1 vv (please enter a decimal) H1 : M1 (Please enter a decimal) b. The test statistic : v v = 0.102 * (please show your answer to 3 decimal places.) c. The p-value = 0.9248 (Please show your answer to 4 decimal places.) d. The p-value is = v a e. Based on this, we should fail to reject vv the null hypothesis. f. Thus, the final conclusion is that .. The results are statistically insignificant at o = 0.10, so there is statistically significantI Question F 1- c The medical researcher is comparing two treatments for lowering cholesterol: diet and meds. The researcher wants to see if the patient: who receive the recommendation to change their diet have less success lowering cholesterol compared to a prescription of meds. A random sample of some patients who received the recommendation to change their diet and others who were prescribed meds was taken. The results of how many did or did not lovver their cholesterol are shown below: Data on Diet vs. Mods for 1l'iiei - ht Loss What can be concluded at the (I = 0.05 level of significance? For this studs. we should use a. The null and alternative hypotheses would be: Hg: [Please enter a decimal? H13 59'9\" 3-" answer V [Pleaie filter a decimal:- b. The test statistic = I I (please show your answer to 3 decimal places.} c. The p-yalue = I I [Please show your answer to 4 decimal places.} d. The p-yalue is D: e. Based on this, we should the null hypothesis. f. Thus_. the final conclusion is that The results are statistically significant at c: = 0.05. so there is sufficient evidence to conclude that the success rate for the I564 patients who received the recommendation to change their diet is less than the success rate for the 333 patient who were prescribed meds. The results are statistically insignificant at c: = 0.05. so we can conclude that the success rate for all patient who receive the recommendation to change their diet is equal to the success rate for all patients who are prescribed meds. The results are statistically significant at c: = 0.05. so there is sufficient evidence to conclude that the population of all patients who received the recommendation to change their diet is less likely to lower their cholesterol than the population of patients who are prescribed meds. The results are statistically insignificant at c: = 0.05. so there is insufficient evidence to conclude that the population of all patients who received the recommendation to change their diet is less likely to lower their cholesterol than the population of patients who are prescribed meds. g. Interpret the p-value in the context of the study. If the success rate for the population of patients who receive the recommendation to change their diet is the same as the success rate for the population of patients who are prescribed meds and if another 6&4 patient: Who are given the recommendation to change their diet and 333 patients who are presclibed meds are surveyed then there would be a 20.46:\"; chance that the percent of the surveyed diet changers who lowered their cholesterol would be at least 1.3.\"; lower than the percent of the surveyed med takers who lowered their cholesterol. There is a 20.45%; chance that patients who receive the change of diet recommendation are 1.3:\": less likely to lower their cholesterol than patients who are prescribed meds. g. Interpret the p-value in the context of the study. '-." If the success rate for the population of patients who receive the recommendation to change their diet is the same as the success rate for the population of patients who are prescribed meds and if another 6:54 patients who are given the recommendation to change their diet and 63?:- patients who are prescribed meds are surveyed then there would be a 20.46.?:' chance that the percent of the sulveyed diet changers who lowered their cholesterol would be at least 1.39: lower than the percent of the surveyed med takers who lowered their cholesterol. '3' There is a 20.4655 chance that patients who receive the change of diet recommendation are 1.6%: less likely to lower their cholesterol than patients who are prescribed meds. '3' There is a 20.4655 chance of a Type I error. '3 If the suocess rate for the sample of patienu who receive the recommendation to change their diet is the same as the success rate for the sample of patients who were prescribed meds and if another :564 patients are given the recommendation to change their diet and 363 patients are prescribed meds then there would be a 20.463? chance of concluding that the success rate for all patients who receive the recommendation to change their diet is at least 1.6% smaller than the success rate for patients who are prescribed meds. h. Interpret the level of significance in the context of the study. 3 If the success rate for the population of patients who receive the recommendation to change their diet is the same as the success rate for the population of patients who are prescribed meds and if another 6:54 patients who are given the recommendation to change their diet and 633 patients who are prescribed meds are surveyed then there would be a 5?. chance that we would end up falsely concuding that the proportion of the 654 patients who received the diet change recommendation who lowered their cholesterol is less than the proportion of the 363 patients who were prescribed meds who lowered their cholesterol. '3 If the suocess rate for the population of patients who receive the recommendation to change their diet is the same as the success rate for the population of patients who are prescribed meds and if another 6:54 patients who are given the recommendation to change their diet and 633 patients who are prescribed meds are surveyed then there would be a 5?. chance that we would end up falsely concuding that the success rate for the population of patients who receive the recommendation to change their diet is less than the success rate for the population of patients who are prescribed meds. 3 There is a 59': chance that a patient won't be able to afford the meds, so they might as well change their diet