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
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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 - Find the appropriate rejection regions for the...Ch. 9.3 - Prob. 9.2ECh. 9.3 - Find the appropriate rejection regions for the...Ch. 9.3 - Prob. 9.4ECh. 9.3 - For the three tests given in Exercise 9.4, use the...Ch. 9.3 - A random sample of n=35 observations from a...Ch. 9.3 - Prob. 9.7ECh. 9.3 - Prob. 9.8ECh. 9.3 - A random sample of 100 observations from a...Ch. 9.3 - Prob. 9.10E
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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- A researcher is interested in examining whether doctors are as accurate at diagnosing certain illnesses via telehealth as they are in person. She randomly assigns a sample of doctors to either see patients via telehealth or in person, and assesses their diagnostic accuracy. What is the null hypothesis for scenario 2? A) H0: µ(telehealth) = µ(in person) =µ(control) B)Ho:μtelehealth=X¯in−person C)H0: rxy = 0 D)H0:µTelehealth =µIn-Personarrow_forwardSuppose a random sample of size 10 is taken from a normally distributed population, and the sample mean and variance are calculated to be x¯=46.1x¯=46.1 and s2=4.5s2=4.5respectively. Use this information to test the null hypothesis H0:μ=50H0:μ=50versus the alternative hypothesis HA:μ≠50HA:μ≠50, at the 5% level of significance. a) What is the value of the test statistic tt, for testing the null hypothesis that the population mean is equal to 50?arrow_forwardLet n1=40, X1=10, n2=40, and X2=20. Complete parts (a) and (b) below. a. At the 0.05 level of significance, is there evidence of a significant difference between the two population proportions? Determine the null and alternative hypotheses. Choose the correct answer below. A. H0: π1≤π2 H1: π1>π2 B. H0: π1≥π2 H1: π1<π2 C. H0: π1≠π2 H1: π1=π2 D. H0: π1=π2 H1: π1≠π2 Calculate the test statistic, ZSTAT, based on the difference p1−p2. The test statistic, ZSTAT, is ? (Type an integer or a decimal. Round to two decimal places as needed.) Calculate the p-value. The p-value is ? (Type an integer or a decimal. Round to three decimal places as needed.) b. Construct a 95% confidence interval estimate of the difference between the two population proportions. ?≤π1−π2≤? (Type integers or decimals. Round to four decimal places as needed.)arrow_forward
- If you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?arrow_forwarda hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with a=0.05 how large does the sample have to bw in order to reject the null hypothesis?arrow_forward
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