At Western University the average scholarship examination scores for freshman applications has been 900. Each year, the assistant dean uses a sample of applications to determine whether the average examination score for the new freshman applications has increased (from the previous year). A random sample of 200 applications was drawn and the average score was found to be 935. Historically, it is known that the score has a Normal distribution and a standard deviation of 180.
a) Identify the parameter of interest.
b) Set up the null hypothesis and the alternative hypothesis.
c) find out the test statistic and find the p-value.
d) Using 5% level of significance level to make an appropriate conclusion so that the Dean could understand.