Problem 2. Suppose that in a large university the marks in an introductory statistics course are normally distribute with a mean of 68 points. To determine the effect of requiring students to pass a calculus test (which is not currently a prerequisite), a random sample of 50 students who have taken calculus given a statistics course. The marks out of 100 were record (see the file Marks.xlsx). Do these data provide evidence (at the 5% level of significance) to infer that students with a calculus background would perform better in statistics than students with no calculus?
Problem 3. Wages and salaries make up only part of a total compensation in the United States. Other parts include paid leave, health insurance, and many others. In 2007, wages and salaries among manufacturers in the United States made up an average of 65.8% of total compensation. To determine if this changed in 2008, a random sample of manufacturing employees was drawn. Can we infer (at the 5% level of significance) that percentage of total compensation for wages and salaries increased between 2007 and 2008? The data recorded in the file Wages.xlsx.
Problem 4. Recent studies seem to indicate that using a cell phone while driving is dangerous. One reason for this is that a driver’s reaction time may slow while he or she is talking on the phone. Researchers measured the reaction times of a sample of drivers who owned a cell phone. Half the sample tested while on the phone and the other half tested while not on the phone. Can we conclude (at the 1% level of significance) that reaction times are slower for drivers using cell phones? The data recorded in the file Drivers.xlsx.