In a large state university (with numerous campuses), the marks in an introductory statistics course are normally distributed with a mean of 68%. To determine the effect of requiring students to pass a calculus test (which at present is not a prerequisite), a random sample of 50 students who have taken calculus is given a statistics course. The marks out of 100 were recorded.
a. Estimate with 95% confidence the mean statistics mark for all students who have taken calculus.
b. Do these data provide evidence to infer that students with a calculus background would perform better in statistics than students with no calculus?