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
5. Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting very good slain removal, good stain removal, and fair stain removal. At a = 0.05, can you conclude that at least one mean cost per ounce is different from the others? (Source: Consumer Reports)
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Elementary Statistics: Picturing the World (6th Edition)
- 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_forwardConduct a test at the a = 0.05 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 p, > p. The sample data are x, = 122, n, = 251, x, = 140, and n, = 301. (a) Choose the correct null and alternative hypotheses below. O A. Ho: p, =p, versus H,: p, P2 (b) Determine the test statistic. Zn = (Round to two decimal places as needed.) (c) Determine the P-value. The P-value isO. (Round to three decimal places as needed.) What is the result of this hypothesis test? O A. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, +p,- O B. Reject the null hypothesis because there is sufficient evidence to conclude that p, p. Click to select your answer(s). Save for Later 4:56 PM Links 12/20/2020arrow_forward
- Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level. The null and alternative hypothesis would be: Ho: PN = HD Ho:µN HD Ho: HN HD HA: HN + HD HẠ:HN > µD HA:HN < HD The test is: two-tailed right-tailed left-tailed The sample consisted of 30 night students, with a sample mean GPA of 2.63 and a standard deviation of 0.4, and 40 day students, with a sample mean GPA of 2.43 and a standard deviation of 0.2. The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals)arrow_forwardIn a statistical test, we have a choice of a left-tailed test, a right-tailed test, or a two-tailed test. Is it the null hypothesis or the alternate hypothesis that determines which type of test is used? Explain your answer. The alternative hypothesis because it specifies what the level of significance of the test will be. The null hypothesis because it specifies what the level of significance of the test will be. The null hypothesis because it specifies the region of interest for the parameter in question. The alternative hypothesis because it specifies the region of interest for the parameter in question.arrow_forwardConduct a test at the a = 0.10 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 fron a jarge population using simple random sampling. Test whether p, > p2. The sample data are x, = 126, n, = 256, x2 = 142, and n2 = 315. (a) Choose the correct null and alternative hypotheses below. O A. Ho: P1 = P2 versus H,: P1 #P2 O B. Ho: P1 = 0 versus H,: P, #0 O C. Ho: P1 =P2 versus H,: P1 P2 (Round to two decimal places as needed.) c) Determine the P-value. The P-value is Round to three decimal places as needed.) Vhat is the result of this hypothesis test? OA. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, # p2- B. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, p,.arrow_forward
- Conduct a test at the a = 0.10 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 p, > p3. The sample data are x, = 116, n, = 259, x, = 133, and n, = 312. (a) Choose the correct null and alternative hypotheses below. O A. Ho: P, = 0 versus H,: p, #0 O B. Ho: P, =p, versus H,: p, P2 O D. Ho: p, =p2 versus H,: p, #P2 b) Determine the test statistic. (Round to two decimal places as needed.) c) Determine the P-value. The P-value is Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion U Do not reject the null hypothesis. O Reject the null hypothesis. Click to select your answer and then click Check Answer. 3 parts remaining Clear All Check Answer 10:26 AM Links 12/20/2020arrow_forwardConduct a test at the a = 0.10 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 p, > P2. The sample data are x, = 121, n, = 259, x, = 140, and n, = 313. (a) Choose the correct null and alternative hypotheses below. O A. Ho: P1 = P2 versus H,: P1 P2 O B. Ho: P1 = P2 versus H,: p1 > P2 O C. Ho: P1 = P2 versus H,:P1 p2. O B. Reject the null hypothesis because there is sufficient evidence to conclude that p, < p,. OC. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, + p2. O D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p,arrow_forwardConduct a test at the a = 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 p, >P2. The sample data are x, = 120, n, = 249, x, = 137, and n, = 312. (a) Choose the correct null and alternative hypotheses below. O A. Ho: P1 = P2 versus H,: P1 #P2 O B. Ho: P1 = P2 versus H,: P1 P2 O D. Ho: P, = 0 versus H,: p, #0 (b) Determine the test statistic. Z, = (Round to two decimal places as needed.) (c) Determine the P-value. The P-value is. (Round to three decimal places as needed.) What is the result of this hypothesis test? O A. Reject the null hypothesis because there is sufficient evidence to conclude that p, p2. OC. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p, # p2. O D. Do not reject the null hypothesis because there is not sufficient evidence to…arrow_forwardRecommended textbooks for you
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