2. A random sample of 9th grade math students was asked if they prefer working their math problems using a pencil or a pen. Of the 250 students surveyed, 100 preferred pencil and 150 preferred pens. a. Using the results of this survey, construct a 95 percent confidence interval for the proportion of 9th grade students that prefer to work their math problems in pen. (3 pts.) b. A school newspaper reported on the results of this survey by saying, "Over half of ninth-grade math students prefer to use pen on their math assignments." Is this statement supported by your confidence interval? Explain. (1 pt.) c. Using the results of this survey, find the minimum sample size required to estimate the true proportion of 9th grade math students who prefer using a pencil, within 1.5% of the true proportion and with 90% confidence. (3 pts.)