SAT scores: The College Board reports that in 2018 the mean score on the math SAT was 527 and the population standard deviation was a 112. A random sample of 20 students who took the test in 2019 had a mean score of 515. Following is a dotplot of the 20 scores. 100 200 300 400 (a) Are the assumptions for a hypothesis test satisfied? 500 600 .. .. 700 D No, the sample size is too small and the sample does not appear to come from a population with an approximately normal distribution. O Yes, the sample size is large enough to perform the test, whether or not the population is normally distributed. O Yes, the sample size is small, but we can see that the sample seems to come from a population with an approximately normal distribution. 100 (b) Perform a hypothesis test to determine whether you can conclude that the mean score in 2019 differs from the mean score in 2018. Assume them population standard deviation is a 112. Use the a=0.05 level of significance and the P-value method with the TI-84 Plus calculator. State the null and alternate hypotheses. H: H : This hypothesis test is a (Choose one) test. left-tailed right-tailed two-tailed X D D O-O Compute the value of the test statistic. Round the answer to two decimal places. H Compute the P-value. Round the answer to at least four decimal places. P-value = X Determine whether to reject Ho. (Choose one) the null hypothesis Ho. Reject Do not reject 5 X State a conclusion. There (Choose one) enough evidence to conclude that the mean score in 2019 differs from the mean score in 2018. is is not