In: Statistics and Probability
1) The average female bobcat weight about 9.6 kg. Let's assume μ = 9.6 and σ = 1.75kg. a) Calculate Pr{Y > 11.5} b) Now assume you have a sample of n = 16 male bobcats. Calculate Pr{ Ȳ > 11.5}. c) Which probability is lower? Why? 2) Refer to problem 1. Now assume you take a sample of n = 9 male bobcats. a) What is the probability of the sample average being within 0.5 kg of the population mean (9.6 kg)? In other words, you need to figure out Pr{ μ - .5 < Ȳ < μ + .5} b) What is the probability of the sample average being within 0.5 kg of the population mean if the population mean is actually μ = 10.8 kg? Are you surprised? Why or why not? You should make sure you understand what happened here. c) Now assume a sample of n = 25 male bobcats and repeat (a). What is the effect of sample size?