Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683416
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 8, Problem 8.2.16RE
To determine
To test: Whether the
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1) Suppose random variable X - N(2,4) (normal distribution with mean 2 and variance 4).
Suppose random variable Y follows the distribution below (0 and 1 are the only two possible
outcomes for Y):
(0.4
Pr(Y %3D у) —
(0.6
What is Pr(X=1) and Pr(Y=1) respectively?
y = 0
y = 1
4 - The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15 mg was found. The expert claims that the amount of chlorine in the water is greater than that measured. For this reason, 100 households were randomly selected, with an average chlorine content of 2.55mg and a variance of 0.49 mg. According to this data, find the account value z.
A) 5,71B) -5,71C) 8,15D) 0,54E) -8,15
Assume a data set D is observed by three models M₁, M2, and M3
which all follow a normal distribution with the variance 4. The
differences between the models are in their means of the distri-
bution which are 2, 4, and 8; respectively. Furthermore, assume
that from prior knowledge we believe p(M₁) = 0.3, p(M₂) = 0.4
and p(M3) = 0.3. Given a data point x = 3.1 which model has a
higher accuracy (or probability to be correct)?
Chapter 8 Solutions
Elementary Statistics: Picturing the World (7th Edition)
Ch. 8.1 - Classify each pair of samples as independent or...Ch. 8.1 - A survey indicates that the mean annual wages for...Ch. 8.1 - A travel agency claims that the average daily cost...Ch. 8.1 - What is the difference between two samples that...Ch. 8.1 - Explain how to perform a two-sample z-test for the...Ch. 8.1 - Describe another way you can perform a hypothesis...Ch. 8.1 - What conditions are necessary in order to use the...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Independent and Dependent Samples In Exercises 58,...
Ch. 8.1 - Prob. 8ECh. 8.1 - In Exercises 9 and 10, use the TI-H4 Plus display...Ch. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - In Exercises 1114, test the claim about the...Ch. 8.1 - In Exercises 1114, test the claim about the...Ch. 8.1 - Prob. 14ECh. 8.1 - Testing the Difference Between Two Means In...Ch. 8.1 - Testing the Difference Between Two Means In...Ch. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Testing the Difference Between Two Means In...Ch. 8.1 - Testing the Difference Between Two Means In...Ch. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Getting at the Concept Explain why the null...Ch. 8.1 - Testing a Difference Other Than Zero Sometimes a...Ch. 8.1 - Testing a Difference Other Than Zero Sometimes a...Ch. 8.1 - Prob. 29ECh. 8.1 - Architect Salaries Construct a 99% confidence...Ch. 8.2 - The annual earnings of 25 people with a high...Ch. 8.2 - A manufacturer claims that the mean driving cost...Ch. 8.2 - What conditions are necessary in order to use the...Ch. 8.2 - Explain how to perform a two-sample t-test for the...Ch. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - In Exercises 38, use Table 5 in Appendix B to find...Ch. 8.2 - Prob. 8ECh. 8.2 - In Exercises 912, test the claim about the...Ch. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - In Exercises 912, test the claim about the...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Constructing Confidence Intervals for 1 2 When...Ch. 8.2 - Constructing Confidence Intervals for 1 2 When...Ch. 8.2 - Constructing Confidence Intervals for 1 2 When...Ch. 8.2 - Prob. 26ECh. 8.2 - How Protein Affects Weight Gain in Overeaters In a...Ch. 8.2 - Prob. 2CSCh. 8.2 - How Protein Affects Weight Gain in Overeaters In a...Ch. 8.2 - Prob. 4CSCh. 8.2 - Prob. 5CSCh. 8.3 - A shoe manufacturer claims that athletes can...Ch. 8.3 - Prob. 2TYCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.4 - Consider the results of the study discussed on...Ch. 8.4 - Prob. 2TYCh. 8.4 - What conditions are necessary in order to use the...Ch. 8.4 - Explain how to perform a two-sample z-test for the...Ch. 8.4 - In Exercises 36, determine whether a normal...Ch. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - In Exercises 36, determine whether a normal...Ch. 8.4 - Prob. 7ECh. 8.4 - Testing the Difference Between Two Proportions In...Ch. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Testing the Difference Between Two Proportions In...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Intermarriages In Exercises 1318, use the figure,...Ch. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Intermarriages In Exercises 1318, use the figure,...Ch. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - U.S. Workforce In Exercises 1922, use the figure...Ch. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8 - Uses Hypothesis Testing with Two Samples...Ch. 8 - Medical research often involves blind and...Ch. 8 - Prob. 8.1.1RECh. 8 - Prob. 8.1.2RECh. 8 - Sample 1: The fuel efficiencies of 20 sports...Ch. 8 - Prob. 8.1.4RECh. 8 - Prob. 8.1.5RECh. 8 - In Exercises 58, test the claim about the...Ch. 8 - Prob. 8.1.7RECh. 8 - In Exercises 58, test the claim about the...Ch. 8 - In Exercises 9 and 10, (a) identify the claim and...Ch. 8 - Prob. 8.1.10RECh. 8 - Prob. 8.2.11RECh. 8 - Prob. 8.2.12RECh. 8 - Prob. 8.2.13RECh. 8 - Prob. 8.2.14RECh. 8 - Prob. 8.2.15RECh. 8 - Prob. 8.2.16RECh. 8 - Prob. 8.2.17RECh. 8 - Prob. 8.2.18RECh. 8 - Prob. 8.3.19RECh. 8 - In Exercises 1922, test the claim about the mean...Ch. 8 - Prob. 8.3.21RECh. 8 - Prob. 8.3.22RECh. 8 - Prob. 8.3.23RECh. 8 - In Exercises 23 and 24, (a) identify the claim and...Ch. 8 - Prob. 8.4.25RECh. 8 - Prob. 8.4.26RECh. 8 - Prob. 8.4.27RECh. 8 - Prob. 8.4.28RECh. 8 - Prob. 8.4.29RECh. 8 - Prob. 8.4.30RECh. 8 - Prob. 1CQCh. 8 - Prob. 2CQCh. 8 - Prob. 3CQCh. 8 - Prob. 4CQCh. 8 - Take this test as you would take a test in class....Ch. 8 - Prob. 2CTCh. 8 - A physical therapist suggests that soft tissue...Ch. 8 - Take this test as you would take a test in class....Ch. 8 - The U.S. Department of Health Human Services...Ch. 8 - Prob. 2RSRDCh. 8 - Prob. 3RSRDCh. 8 - Prob. 4RSRDCh. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - In Exercises 36, construct the indicated...Ch. 8 - In Exercises 36, construct the indicated...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 14CRCh. 8 - Prob. 15CRCh. 8 - Prob. 16CRCh. 8 - A researcher claims that 5% of people who wear...
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- Let Y1, Y2,..., Y; be a random sample of size 5 from a normal population with mean 0 and variance 1 and let Y = (1/5) Y;. Let Y, be another independent observation from the same population. What is the distribution of 7.37 a W = E Y? Why? b U = E- (Y; – Y)?? Why? c E- (Y; – Y)² + Y?? Why? i3D1arrow_forward7) Consider the computer output shown below: One-Sample T: Y Test of mu = 91 vs. not = 91 Variable N Mean Std. Dev. SE Mean 95% CI т 25 92.5805 0.4675 (91.6160, ? ) 3.38 0.002 (d) What is the P-value if the alternative hypothesis is H,: u> 91?arrow_forwardTest the claim about the difference between two population means u, and H2 at the level of significance oa. Assume the samples are random and independent, and the populations are normally distributed. Claim: 4, SH2; a= 0.05. Assume o #o, Sample statistics: x, = 2417, s, = 177, n, 12 and X2 = 2296, s2 = 55, n2 = 11 Identify the null and alternative hypotheses. Choose the comrect answer below. O D. Ho: H1 SH2 Find the standardized test statistic t. = 1 (Round to two decimal places as needed.) Find the P-value. D=d (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.arrow_forward
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- 2. A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school diploma is 0.87. a) Suppose you took a simple random sample of 100 young Americans. We know because of sampling variability that the sample proportion of those who earned a high school diploma would vary each time you took a sample. Assuming the value above can be taken as the population proportion (i.e., as a parameter), what model can be used to describe how these sample proportions would vary? Please be sure to include the name of the distribution and the parameter values. See pg. 131 in the Class Notes. b) Find the probability that 89% or more in the sample will have earned a high school diploma.arrow_forwardFor a hypothesis test H0:μ=6H0:μ=6 versus H1:μ≠6H1:μ≠6 and variance known, calculate the p-value for the test statistics: (4 d.p.) i) zc=2.05 ii) zc = -1.84 iii) zc = 2.86arrow_forwardTwo samples were drawn independently from two normal populations. Sample 1: 11.6, 11.35, 10.1, 10.85, 10.35, 10.6, and 11.1.Sample 2: 5.85, 8.85, 9.85, 11.85 and 7.85.Test to determine whether the means of the two population differs (use α=0.05).arrow_forward
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