In: Statistics and Probability
The grade of statistics follows a normal distribution with a
mean of 85 and a
standard deviation of 10. The instructor adopted a new teaching
method this year,
and would like to investigate whether there is an improvement in
students’
average grade. Suppose the average grade from a sample of 36
students is 88, can
we conclude that there is an improvement at the 5% significance
level?
A. Specify the null and alternative hypotheses.
B. Determine the rejection region.
C. Calculate the test statistics.
D. Make a decision regarding the null hypothesis.
E. Report the conclusion.
F. Describe what a Type I Error would be in this scenario, and what
the
consequence might be for the teacher.