Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 2.3, Problem 55E
To determine
To find: The
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Consider the state space model X₁ = §Xt−1 + Wt, Yt
=
AX+Vt, where Xt
Є R4
and Y E R². Suppose we know the covariance matrices for Wt and Vt. How many
unknown parameters are there in the model?
Business Discuss
You want to obtain a sample to estimate the proportion of a population that possess a particular genetic marker. Based on previous evidence, you believe approximately p∗=11% of the population have the genetic marker. You would like to be 90% confident that your estimate is within 0.5% of the true population proportion. How large of a sample size is required?n = (Wrong: 10,603)
Do not round mid-calculation. However, you may use a critical value accurate to three decimal places.
Chapter 2 Solutions
Introduction to the Practice of Statistics
Ch. 2.1 - Prob. 1UYKCh. 2.1 - Prob. 2UYKCh. 2.1 - Prob. 3UYKCh. 2.1 - Prob. 4UYKCh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.2 - Prob. 10UYK
Ch. 2.2 - Prob. 11UYKCh. 2.2 - Prob. 12UYKCh. 2.2 - Prob. 13UYKCh. 2.2 - Prob. 14UYKCh. 2.2 - Prob. 15UYKCh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.3 - Prob. 38UYKCh. 2.3 - Prob. 39UYKCh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.4 - Prob. 61UYKCh. 2.4 - Prob. 62UYKCh. 2.4 - Prob. 63UYKCh. 2.4 - Prob. 64UYKCh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.4 - Prob. 71ECh. 2.4 - Prob. 72ECh. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Prob. 78ECh. 2.4 - Prob. 79ECh. 2.4 - Prob. 80ECh. 2.4 - Prob. 81ECh. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Prob. 87ECh. 2.4 - Prob. 88ECh. 2.4 - Prob. 89ECh. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.5 - Prob. 92UYKCh. 2.5 - Prob. 93UYKCh. 2.5 - Prob. 94ECh. 2.5 - Prob. 95ECh. 2.5 - Prob. 96ECh. 2.5 - Prob. 97ECh. 2.5 - Prob. 98ECh. 2.5 - Prob. 99ECh. 2.5 - Prob. 100ECh. 2.5 - Prob. 101ECh. 2.5 - Prob. 102ECh. 2.5 - Prob. 103ECh. 2.5 - Prob. 104ECh. 2.5 - Prob. 105ECh. 2.5 - Prob. 106ECh. 2.5 - Prob. 107ECh. 2.5 - Prob. 108ECh. 2.5 - Prob. 110ECh. 2.5 - Prob. 111ECh. 2.5 - Prob. 112ECh. 2.6 - Prob. 113UYKCh. 2.6 - Prob. 114UYKCh. 2.6 - Prob. 115UYKCh. 2.6 - Prob. 116UYKCh. 2.6 - Prob. 117UYKCh. 2.6 - Prob. 118UYKCh. 2.6 - Prob. 119ECh. 2.6 - Prob. 120ECh. 2.6 - Prob. 121ECh. 2.6 - Prob. 122ECh. 2.6 - Prob. 123ECh. 2.6 - Prob. 124ECh. 2.6 - Prob. 125ECh. 2.6 - Prob. 126ECh. 2.6 - Prob. 127ECh. 2.6 - Prob. 128ECh. 2.6 - Prob. 129ECh. 2.6 - Prob. 130ECh. 2.7 - Prob. 131ECh. 2.7 - Prob. 132ECh. 2.7 - Prob. 133ECh. 2.7 - Prob. 134ECh. 2.7 - Prob. 135ECh. 2.7 - Prob. 136ECh. 2.7 - Prob. 137ECh. 2.7 - Prob. 138ECh. 2.7 - Prob. 139ECh. 2.7 - Prob. 140ECh. 2.7 - Prob. 141ECh. 2.7 - Prob. 142ECh. 2.7 - Prob. 143ECh. 2 - Prob. 144ECh. 2 - Prob. 145ECh. 2 - Prob. 146ECh. 2 - Prob. 147ECh. 2 - Prob. 148ECh. 2 - Prob. 149ECh. 2 - Prob. 150ECh. 2 - Prob. 151ECh. 2 - Prob. 152ECh. 2 - Prob. 153ECh. 2 - Prob. 154ECh. 2 - Prob. 155ECh. 2 - Prob. 156ECh. 2 - Prob. 157ECh. 2 - Prob. 158ECh. 2 - Prob. 159ECh. 2 - Prob. 160ECh. 2 - Prob. 161ECh. 2 - Prob. 162ECh. 2 - Prob. 163ECh. 2 - Prob. 164ECh. 2 - Prob. 165ECh. 2 - Prob. 166ECh. 2 - Prob. 167ECh. 2 - Prob. 168ECh. 2 - Prob. 169ECh. 2 - Prob. 170ECh. 2 - Prob. 171ECh. 2 - Prob. 172ECh. 2 - Prob. 173ECh. 2 - Prob. 174ECh. 2 - Prob. 175ECh. 2 - Prob. 176E
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- 2. [20] Let {X1,..., Xn} be a random sample from Ber(p), where p = (0, 1). Consider two estimators of the parameter p: 1 p=X_and_p= n+2 (x+1). For each of p and p, find the bias and MSE.arrow_forward1. [20] The joint PDF of RVs X and Y is given by xe-(z+y), r>0, y > 0, fx,y(x, y) = 0, otherwise. (a) Find P(0X≤1, 1arrow_forward4. [20] Let {X1,..., X} be a random sample from a continuous distribution with PDF f(x; 0) = { Axe 5 0, x > 0, otherwise. where > 0 is an unknown parameter. Let {x1,...,xn} be an observed sample. (a) Find the value of c in the PDF. (b) Find the likelihood function of 0. (c) Find the MLE, Ô, of 0. (d) Find the bias and MSE of 0.arrow_forward3. [20] Let {X1,..., Xn} be a random sample from a binomial distribution Bin(30, p), where p (0, 1) is unknown. Let {x1,...,xn} be an observed sample. (a) Find the likelihood function of p. (b) Find the MLE, p, of p. (c) Find the bias and MSE of p.arrow_forwardGiven the sample space: ΩΞ = {a,b,c,d,e,f} and events: {a,b,e,f} A = {a, b, c, d}, B = {c, d, e, f}, and C = {a, b, e, f} For parts a-c: determine the outcomes in each of the provided sets. Use proper set notation. a. (ACB) C (AN (BUC) C) U (AN (BUC)) AC UBC UCC b. C. d. If the outcomes in 2 are equally likely, calculate P(AN BNC).arrow_forwardSuppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values for normal probability plots. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0.191 0.186 0.201 0.2005 0.203 0.210 0.234 0.248 0.260 0.273 0.281 0.290 0.305 0.310 0.308 0.311 Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) ○ A. Yes. The correlation between the expected z-scores and the observed data, , exceeds the critical value, . Therefore, it is reasonable to conclude that the data come from a normal population. ○…arrow_forwardding question ypothesis at a=0.01 and at a = 37. Consider the following hypotheses: 20 Ho: μ=12 HA: μ12 Find the p-value for this hypothesis test based on the following sample information. a. x=11; s= 3.2; n = 36 b. x = 13; s=3.2; n = 36 C. c. d. x = 11; s= 2.8; n=36 x = 11; s= 2.8; n = 49arrow_forward13. A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Would the manager of the pharmaceutical company be more concerned about a Type I error or a Type II error? Explain.arrow_forwardFind the z score that corresponds to the given area 30% below z.arrow_forwardFind the following probability P(z<-.24)arrow_forward3. Explain why the following statements are not correct. a. "With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error." b. "I have already decided how much of the Type I error I am going to allow. A bigger sample will not change either the Type I or Type II error." C. "I can reduce the Type II error by making it difficult to reject the null hypothesis." d. "By making it easy to reject the null hypothesis, I am reducing the Type I error."arrow_forwardGiven the following sample data values: 7, 12, 15, 9, 15, 13, 12, 10, 18,12 Find the following: a) Σ x= b) x² = c) x = n d) Median = e) Midrange x = (Enter a whole number) (Enter a whole number) (use one decimal place accuracy) (use one decimal place accuracy) (use one decimal place accuracy) f) the range= g) the variance, s² (Enter a whole number) f) Standard Deviation, s = (use one decimal place accuracy) Use the formula s² ·Σx² -(x)² n(n-1) nΣ x²-(x)² 2 Use the formula s = n(n-1) (use one decimal place accuracy)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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