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1. Consider the data set below, which gives a sample of fifteen students randomly selected and asked the number of students in their statistics class. 34 45 27 33 38 41 30 39 34 40 28 33 45 29 36 (a) Find the 90% confidence interval for the mean number of students in a statistics class. (b) Find the 95% confidence interval for the mean number of students in a statistics class. (c) Find the 99% confidence interval for the mean number of students in a statistics class. (d) Interpret your 95% confidence interval in context of the data. (e) Based on the intervals you calculated, do you think it is reasonable to conclude that the mean number of students in a statistics class is greater than 30 students? Explain your reasoning. (1') Using the sample standard deviation of the data given in this problem, calculate the sample size needed to produce an 85% confidence interval with a margin of error of 3.5