Problem 9 Using the information provided in #8, find the smallest sample size needed to estimate , with a margin of error no larger than 2, with 90% confidence. Problem 10 At the beginning of the semester, the instructor of a large statistics class assigns students to study groups of 5 students each. A sample is selected by randomly selecting 7 study groups and asking each student in these selected groups to provide the time (in minutes) they spend texting each day. Surprisingly the sample of 35 is not strongly skewed and does not have outliers. The sample mean and standard deviation are x = 20.3 minutes and s = 4.9 minutes, respectively. a) Identify the sampling technique. b) Construct and interpret the 90% confidence interval for = the population mean amount of time students in this large statistics class spend texting. Problem 11 Suppose 44 Purdue students are selected using technology which randomly generated their PUID and asked what their favorite subject is. 15 students say Statistics is their favorite subject. a) Identify the sampling technique. b) Construct and interpret the 95% confidence interval for p = the population proportion of Purdue students who say Statistics is their favorite subject. Problem 12 Consider the sample proportion provided in #11 to be from a pilot study. Find the smallest sample size needed to estimate p, with a margin of error no larger than 0.03, with 99% confidence. Problem 7 Referring to #6, suppose a sample of 20 is selected by randomly choosing four keyboardists from each of the five business majors at a university. Let X = the mean net keyboarding rate of the 20 keyboardists. a) Which sampling technique was used? b) Is X a continuous or discrete random variable? c) What is the shape of the sampling distribution of X? d) What is the mean of the sampling distribution of X? e) What is the standard error of the sampling distribution of X? f) Find: P(X > 80) P(45 < x 80) P(45X55) c) Find the wpm rate needed to be considered the slowest 5% (which would be the lowest 5% of rates, or the 5th percentile).