1. a researcher has performed extensive research on the effects of
formed extensive research on the effects of caffeine on students in a math
class. the researcher consistently
consistently finds that caffeine improves students performances in the
math class. this leads the researcher to believe that caffeine will also improve students' performance in the in an english class. the researcher contacts an english instructor who has given the same final exam to his students for many years. the mean score that students have obtained
on the final exam is 100 with a standard deviation of 12. the researcher randomly selects 50 students and has each consume 100 mg of caffeine prior to the final exam. the mean score of the
50 caffeinated students on the final exam is 96.4. test whether the sample mean is significantly greater than the population mean at the .05 level of significance.
b find the critical values of the test statistic.