Identify hypotheses, Part I. Write the null and alternative hypotheses in words and then symbols for each of the following situations. (a) A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their services. They sample 200 of the students who used their service in the past year and ask them if their grades have improved from the previous year. Null Hypothesis: Grades have not improved for any students. Grades have not improved for a majority of students. Grades have improved for all students. Grades have improved for a majority of students. Alternative Hypothesis: Grades have not improved for any students. Grades have improved for all students. Grades have not improved for a majority of students. Grades have improved for a majority of students. H0: p < 0.5 p = 1 p > 0 p = 0 p < 1 p > 0.5 p = 0.5 H1: p > 0.5 p = 0.5 p = 0 p < 0.5 p < 1 p > 0 p = 1 (b) Employers at a firm are worried about the effect of March Madness, a basketball championship held each spring in the US, on employee productivity. They estimate that on a regular business day employees spend on average 15 minutes of company time checking personal email, making personal phone calls, etc. They also collect data on how much company time employees spend on such non-business activities during March Madness. They want to determine if these data provide convincing evidence that employee productivity changed during March Madness. Null Hypothes