5. In Alaska, a random sample of 15 eight-grade students has a mean score of 265 with a sample standard deviation ...

5. In Alaska, a random  sample of 15 eight-grade  students  has a mean score of 265 with a sample standard deviation of 55 on a national  mathematical assessment test. This prompts  a state  school administrator to declare  that  the mean score is more than 260.  At a five percent  significance level, is there  enough evidence to support the administrator's claim? Assume the population  standard deviation is unknown; use the "t" procedure. (6 points)

6. In  a  simple  random  sample  of  42 Alaskan  civil engineering  firms  the  mean number  of employees is sixteen.  The population standard deviation is estimated  to be four  employees.  Establish  the  95.5%  confidence  interval  for  the  population mean.  Assume the population  standard deviation is known;  use the "z" procedure. (5 points)