The National Association of Educational Progress (NAEP) quantitative score for all NAEP test takers has a mean score of 275. In a survey of 840 young men, there is a mean score of 270. Researchers believe this score represents a decline in male performance.
The population standard deviation is known to be 60.
a. Is this score significant at the 1% level of significance?
b. Based on your results, is there a likelihood of a Type I or a Type II error? What is the probability of that error?