\f7. An educational study in 2020 found that the average score on a normalized achievement exam given nationally to fth grade students was 38.6. A state school board, after implementing new curriculum, believes the average score is signicantly higher for the fth grade students in their state, possibly due to this new curriculum. In an effort to statistically establish this claim, the state board randomly samples forty fth graders, examining their scores on the achievement exam. The scores appear below. Is there sufcient evidence at the 0.10 level to substantiate the state school board's claims? 47 35 37 49 41 41 36 45 22 55 41 38 40 40 41 37 51 30 43 50 32 29 53 52 40 43 36 33 46 44 49 41 22 32 4B 38 35 30 43 53 a. Give the null and alternative hypotheses for this test. H0: H1: b. Determine the value of the test statistic. 8. A registered nurse (RN) desires her local nursing staff to be more consistent in the care of patients needs than nursing staff at other hospitals. A national nursing organization claims that the score patients give, on average, to nurses across the nation on a "care survey" is 122 points with a standard deviation of 45 points. To test her staff's performance, the RN randomly selects fty patients during the last two months and receives "care survey" responses from those patients. The standard deviation of this sample group is found to be 41. Use an appropriate hypothesis test at the 5% signicance level to determine if the RN should conclude that the consistencv in care bv her staff is better than the national care (as measured bv a statisticallv signicant smaller standard deviation a. Give the null and alternative hypotheses for this test in symbolic form. H0: H1: b. After applying a correct hypothesis test, write a statement to give the RN, explaining the results of the hypothesis test. Make your statement tie to the context of the patient care survey question of variability in measures