Use the values in the table below, which represent the heights (in centimeters) of 30 randomly selected college students, to answer Parts a) through c): 172 165 179 183 168 175 182 177 163 169 166 171 174 178 186 168 170 173 175 177 164 167 172 176 181 188 169 173 167 164 a) Estimate,with89%confidence,theproportionofallstudentsenrolledinthecollege who are at least 175 cm tall. (1 point) QMETH 201, Homework 5 b) How would the width of the interval in Part a) change if you wanted to be 95% confident, holding all other values/ideas constant? (0.5 points) c) Howwouldthewidthoftheintervalinparta)changeifwedecreasedthesamplesizeto 20 students, holding all other values/ideas constant? (0.5 points) d) For the 30 students in the sample, calculate the mean height (in centimeters) and the sample standard deviation. (Use MS Excel to perform calculations.) Then estimate, with 98% confidence, the mean height (in cm) for all college students. (You can use Excel or a graphing calculator to calculate standard deviation.) (1 point) e) How would the width of the interval in part d) change if we lowered the standard deviation, holding all other values/ideas constant? (0.25 point)