Performing a One-Way ANOVA Test In Exercises 5−14, (a) identify the claim and state H0 and Ha. (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are
11. Well-Being Index The well-being index is a way to measure how people are faring physically, emotionally, socially, and professionally, as well as to rate the overall quality of their lives and their outlooks for the future. The table shows the well-being index scores for a sample of states from four regions of the United States. At a = 0.10, can you reject the claim that the mean score is the same for all regions? (Adapted from Gallup and Healthways)
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MYLAB STATISTICS: ELEMENTARY STATISTICS
- Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forwardWhat is meant by the sample space of an experiment?arrow_forwarddashratharrow_forward
- Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Using a 0.05 significance level, test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. H2 In 25 25 0.52 0.46 S 0.75 1.43 What are the null and alternative hypotheses? O A. Ho: H1 H2 O D. Ho: H1 # H2 H1: 41arrow_forwardRandom selection of two independent samples of sizes n1= 12 and n2 = 12 are given. Which procedure should be applied to perform a hypothesis test to compare the means of the two populations from which the data were obtained.arrow_forward(a) identify the claim and state H(o) and H(a) (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, (d) interpret the decision in the context of the original claim. Assume the population is normally distributed. Dive Duration An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.5 minutes. A random sample of 34 dive durations has a mean of 12.2 minutes and a standard deviation of 2.2 minutes. Is there enough evidence to reject theclaim at a = 0.10?arrow_forward(a) Identify the claim and state H0 and Ha.What is the claim? Let Region A be sample 1 and let Region B be sample 2. Identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region. What is the rejection region? (c) Find the standardized test statistic z. (d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.arrow_forwardFor the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent. Claim: µ,arrow_forwardUse the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha: H1 H2, a= 0.01, n, = 12, n2 = 10 (a) Find the critical value(s) assuming that the population variances are equal. 2.845,2.845 (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) (b) Find the critical value(s) assuming that the population variances are not equal. (Týpe an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)arrow_forward(b) Use technology to find the P-value. (c) Decide whether to reject or fail to reject the null hypothesis. (d) Interpret the decision in the context of the original claim.arrow_forwardConduct a test at the α= 0.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1 > p2 . The sample data are x1 = 122, n1 = 241, x2 = 132, and n2 = 314. Choose the correct null and alternative hypotheses H0 : p1 = p2 versus H1 : p1 > p2 H0 : p1 = 0 versus H1 : p1 ≠ 0 H0 : p1 = p2 versus H1 : p1 ≠ p2 H0 : p1 = p2 versus H1 : p1 < p2 Determine the test z0 = _______________ (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of this hypothesis test? Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1 < p2 . Reject the null hypothesis because there is sufficient evidence to conclude that p1 < p2 . Do not reject the null…arrow_forwardTest the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. Show step1-step3 include a conclusion.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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