EBK ESSENTIAL STATISTICS FOR THE BEHAVI
2nd Edition
ISBN: 9781506386287
Author: PRIVITERA
Publisher: VST
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Chapter 3, Problem 19CAP
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The best measure of
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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.
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.
Chapter 3 Solutions
EBK ESSENTIAL STATISTICS FOR THE BEHAVI
Ch. 3 - Prob. 1FPCh. 3 - Prob. 2FPCh. 3 - Prob. 3FPCh. 3 - Prob. 4FPCh. 3 - Prob. 5FPCh. 3 - Prob. 6FPCh. 3 - Prob. 7FPCh. 3 - Prob. 8FPCh. 3 - Prob. 9FPCh. 3 - Prob. 10FP
Ch. 3 - Prob. 11CAPCh. 3 - Prob. 12CAPCh. 3 - Prob. 13CAPCh. 3 - Prob. 14CAPCh. 3 - Prob. 15CAPCh. 3 - Prob. 16CAPCh. 3 - Prob. 17CAPCh. 3 - Prob. 18CAPCh. 3 - Prob. 19CAPCh. 3 - Prob. 20CAPCh. 3 - Prob. 21CAPCh. 3 - Prob. 22CAPCh. 3 - Prob. 23CAPCh. 3 - Prob. 24CAPCh. 3 - Prob. 25CAPCh. 3 - Prob. 26CAPCh. 3 - Prob. 27CAPCh. 3 - Prob. 28CAPCh. 3 - Prob. 29PRCh. 3 - Prob. 30PRCh. 3 - Prob. 31PRCh. 3 - Prob. 32PRCh. 3 - Prob. 33PR
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- 1. [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_forwardTable of hours of television watched per week: 11 15 24 34 36 22 20 30 12 32 24 36 42 36 42 26 37 39 48 35 26 29 27 81276 40 54 47 KARKE 31 35 42 75 35 46 36 42 65 28 54 65 28 23 28 23669 34 43 35 36 16 19 19 28212 Using the data above, construct a frequency table according the following classes: Number of Hours Frequency Relative Frequency 10-19 20-29 |30-39 40-49 50-59 60-69 70-79 80-89 From the frequency table above, find a) the lower class limits b) the upper class limits c) the class width d) the class boundaries Statistics 300 Frequency Tables and Pictures of Data, page 2 Using your frequency table, construct a frequency and a relative frequency histogram labeling both axes.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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