The National Assessment of Educational Progress (NAEP) includesa mathematics test for eighth‑grade students. Scores on the testrange from 0 to 500 . Demonstrating the ability to use the mean tosolve a problem is an example of the skills and knowledgeassociated with performance at the Basic level. An example of theknowledge and skills associated with the Proficient level is beingable to read and interpret a stem‑and‑leaf plot. In 2015, 136,900eighth‑graders were in the NAEP sample for the mathematics test.The mean mathematics score was ?¯=282 . We want to estimate themean score ? in the population of all eighth‑graders. Consider theNAEP sample as an SRS from a Normal population with standarddeviation ?=110 . (a) If we take many samples, the sample mean ?¯varies from sample to sample according to a Normal distributionwith mean equal to the unknown mean score ? in the population. Whatis the standard deviation of this sampling distribution? (Enteryour answer rounded to four decimal places.)
(c) What is the 95% confidence interval for the population meanscore ? based on this one sample? (Enter your answer rounded to onedecimal place.)
Lower value =
Higher value=
