Introduction to Probability and Statistics
Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 9.4, Problem 9.20E
To determine

To explain: Probability of α that will incorrectly reject H0 .

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Method A: M1= 54, SS1= 400, n1= 15  Method B: M2=40, SS2= 440, n2=15 Using alpha=0.05 should the null hypothesis by rejected for the above data?
A random sample of n1=17�1=17 securities in Economy A produced mean returns of x̄ 1=5.6% x̄ 1=5.6% with s1=2.3%�1=2.3% while another random sample of n2=20�2=20 securities in Economy B produced mean returns of x̄ 2=4.6% x̄ 2=4.6% with s2=2.3%.�2=2.3%. At α =0.2 α =0.2, can we infer that the returns differ significantly between the two economies? Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 12= σ 22)( σ 12= σ 22). T-Distribution Table a. Calculate the test statistic. t=�=   Round to three decimal places if necessary b. Determine the critical value(s) for the hypothesis test. + Round to three decimal places if necessary c. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject
1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μand V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean:ˆμ1 = (n −3/n) ̄Xˆμ2 = 0.95 ̄X(a) Which of the estimators is an unbiased estimator for μ?(b) Which is the variance of the two estimators?(c) Given the properties above, which one would you prefer? Is there another property that wouldinfluence your decision? Explain.

Chapter 9 Solutions

Introduction to Probability and Statistics

Ch. 9.3 - Prob. 9.11ECh. 9.3 - Prob. 9.12ECh. 9.3 - Prob. 9.14ECh. 9.3 - Prob. 9.15ECh. 9.3 - What’s Normal? What is normal, when it comes to...Ch. 9.4 - Prob. 9.18ECh. 9.4 - Independent random samples of 36 and 45...Ch. 9.4 - Prob. 9.20ECh. 9.4 - Cure for the Common Cold? An experiment was...Ch. 9.4 - Healthy Eating As Americans become more conscious...Ch. 9.4 - Prob. 9.24ECh. 9.4 - Prob. 9.25ECh. 9.4 - Prob. 9.26ECh. 9.4 - Prob. 9.27ECh. 9.4 - Prob. 9.28ECh. 9.4 - What’s Normal II Of the 130 people in Exercise...Ch. 9.5 - A random sample of n=1000 observations from a...Ch. 9.5 - A random sample of n=1400 observations from a...Ch. 9.5 - Prob. 9.32ECh. 9.5 - Prob. 9.33ECh. 9.5 - Prob. 9.38ECh. 9.5 - Prob. 9.40ECh. 9.5 - Prob. 9.41ECh. 9.6 - Independent random samples of n1=140 and n2=140...Ch. 9.6 - Prob. 9.43ECh. 9.6 - Prob. 9.46ECh. 9.6 - Prob. 9.47ECh. 9.6 - Prob. 9.48ECh. 9.6 - Prob. 9.49ECh. 9.6 - Prob. 9.50ECh. 9 - Prob. 9.52SECh. 9 - Prob. 9.53SECh. 9 - Prob. 9.54SECh. 9 - Prob. 9.55SECh. 9 - Prob. 9.56SECh. 9 - Prob. 9.57SECh. 9 - Prob. 9.58SECh. 9 - Prob. 9.59SECh. 9 - Prob. 9.60SECh. 9 - White-Tailed Deer In an article entitled “A...Ch. 9 - Prob. 9.62SECh. 9 - Prob. 9.63SECh. 9 - Prob. 9.64SECh. 9 - Prob. 9.65SECh. 9 - Prob. 9.66SECh. 9 - Prob. 9.67SECh. 9 - Prob. 9.68SECh. 9 - Prob. 9.69SECh. 9 - Prob. 9.70SECh. 9 - Prob. 9.71SECh. 9 - Actinomycin D A biologist hypothesizes that high...Ch. 9 - Prob. 9.73SECh. 9 - Prob. 9.74SECh. 9 - Heights and Gender It is a well-accepted fact that...Ch. 9 - Prob. 9.79SECh. 9 - Prob. 9.81SE
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