Exercise 14.36 The 14 deer mice had average body length of 91.1 mm. Assume that the standard deviation of body lengths in the population of all deer mice in the rich forest habitat is the same as that of the general deer mouse population and is equal to 8mm. Estimate the mean body length of all deer mice. Different ways in which the same question can be worded. 1. What is the mean body length of deer mice? Note that we can never find the true/actual/population mean, we can only estimate it using a confidence interval. 2. What is the average body length of deer mice? Note that we can never find the true/actual/population mean, we can only estimate it using a confidence interval. 3. What is the body length of deer mice? We can never find the true mean/average body length. Although the question does not say the word "mean" or "average", we still need to estimate the mean/average body length and estimating the mean body length is the only way to answer this question. First let us answer the following questions and do the calculations for the confidence interval. Once this is done we will write the four step process in the next question. First note the following. x = the variable = Description of we are measuring in this study n = Sample size = Number of individuals in the observational or experim x = x bar = Mean or Average of the measurement in the sample = Sam H = Mean or Average of the Population = Population Mean s = sx = Standard Deviation of the sample == Sample Standard Deviatio C- Confidene level - Choose 90% or 95% z - Can be found from Table C based on the confidence level If σ is given then we use z - procedures to construct a confidence interval u √n (x- x + √n √n x - Body length of deer mice What are we going to estimate in this problem? (xbar / Mu) Is Population Standard Deviation (0) given? the difference between sigma and s) (Yes/No) (This question is for you to stop and think about Is Population Standard Deviation (σ) given? the difference between sigma and s) σ = n = 12 x mm (Yes/No) (This question is for you to stop and think about = mm in (Use Crunchit > Chapter 14 Table 1 > Descriptive Statistics. Write the number with two decimal places) If c = 95% then z* = Calculate the confidence interval using the formula. The 95% confidence interval is (1, 2). (Note that we write the smaller number first and the larger number next because it is a range of values) 1 = mm (Round to two decimal places) 2 = mm (Round to two decimal places)