Concept explainers
In Exercises 9–12, test the claim about the difference between two population
9. Claim: μ1 = μ2; α = 0.01, Assume,
Sample statistics:
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Elementary Statistics: Picturing the World (7th Edition)
- 3.STATISTICAL INFERENCEarrow_forwardA state-by-state survey found that the proportions of adults who are smokers in state A and state B were 23.1% and 17.2%, respectively. (Suppose the number of respondents from each state was 2000.) At α=0.05, can you support the claim that the proportion of adults who are smokers is greater in state A than in state B? Assume the random samples are independent. Complete parts (a) through (e).arrow_forwardLet 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_forward
- Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At α=0.10, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below.arrow_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_forwardTest the claim about the difference between two population means u, and u, at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: H, SHz; a = 0.10. Assume o, #o, Sample statistics: x, = 2418, s, = 179, n, = 15 and X2 = 2295, s, = 55, n, =9 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: H1> H2 Ha: H1 SH2 O B. Ho: H1 2H2 Ha: H1 H2 O D. Ho: H1arrow_forward22. In an attempt to compare the durability of two different materials (X and Y), 10 pieces of type X and 14 pieces of type Y were used. From these samples we calculate the statistics: X= 129.44, y = 122.65, sx = 9.15, sy = 11.02. Assuming the two populations sampled are normal with equal variance, find the P-value. (0.05, 0.10) (0.01,0.025) (0.02,0.05). (0.1,0 2)arrow_forward2.STATISTICAL INFERENCEarrow_forwardTest the claim about the difference between two population means H, and u2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: 41 SH2; a = 0.10. Assume o, #o, Sample statistics: X, = 2417, s, = 179, n, = 12 and X2 = 2296, s2 = 53, n2 = 10 Identify the null and alternative hypotheses. Choose the correct answer below. 대= 내 : "H OF. Ho: H1 2H2 Find the standardized test statistic t. (Round to two decimal places as needed.) Find the P-value. (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. V Ho. There V enough evidence at the 10% level of significance to reject the claim.arrow_forward2. Research groups A and B have studied independently a phenomenon that can be described by random sampling from a normal distribution N(μ, σ²), where both parameters are unknown. The interesting parameter is is the population average μ. Results of research groups (sample size, sample mean and sample variance) are respectively nA = 10, NB = 15, A = 3.967, s B = 3.522, s = 1.995, = 1.310. We would like to do meta analysis, i.e. combine the research results of these two groups. We set the hypotheses H₁: µ = 3 and H₁: µ 3. Hypotheses are tested using a two-sided t-test and significance level 0.05. (a) Calculate the usual point estimater for the parameters μ and σ² by using the data sets of both group A and group B. (First determine nA+B, A+B and s² A+B using the given information¹ on the data sets.) (b) Test the hypotheses using the data of the group A (α = 0.05). State the p-value of the test and the decision of rejecting or accepting the null hypothesis. (c) Test the hypothesis using…arrow_forwardTest the claim about the difference between two population means u, and p2 at the level of significance a. Assume the samples random and independent, and the populations are normally distributed. Claim: 4, SHzi a= 0.10. Assume o #o Sample statistics: X1 = 2418, s, = 174, n, = 12 and X2 = 2291, s2 = 54, n2 = 10 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: Hi # H2 O C. Ho: Hy Hz Find the standardized test statistic t. (Round to two decimal places as needed.) Find the P-value. (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_forward3. Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill