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In Exercises 9–12, test the claim about the difference between two population
12. Claim: μ1 > μ2; α = 0.01, Assume
Sample statistics:
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Elementary Statistics: Picturing the World (7th Edition)
- 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_forward2.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_forward
- 2. 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_forward10. Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. Claim: μ<4915; α=0.05 Sample statistics: x=5017, s=5613, n=55 Question content area bottom Part 1 What are the null and alternative hypotheses? H0: muμ greater than or equals≥ 4915 4915 Ha: muμ less than< 4915 4915 (Type integers or decimals. Do not round.) Part 2 Find the standardized test statistic t. t=enter your response here (Round to two decimal places as needed.)arrow_forward2. 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_forward
- 22. 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_forward7. Assume we have two independent population random variables, X and Y. We have samples from each population with n = 70.1, g = 75.3 and their sample variances, s? = 60, s? = 40. Then construct one-sided 95% confidence intervals for µx – µy. 30 and m %3D Пү 40 having a %3|arrow_forward2. Independent random samples, each of size n = 395, selected from two populations produced the sample means and standard deviations shown below: Sample 1: FT = 5, 287, and s1 = 149 Sample 2: = 5, 252, and s2 = 203 In order to compare the means of the two populations, test Ho : (41 - H2) = 0 against Ha : (1 - 12) + 0, using a = 0.05. (a) The value of the test statistic 24 (rounded to two decimal places) is (i) -1.81 (ii) 0.58 (iii) 1.43 (iv) 2.76 (b) The p-value (rounded to four decimal places) is (i) 0.9971 (ii) 0.0029 (iii) 0.0058 (iv) 0.0702 You should find one of the following useful for part b: P(z > 1.43) = 0.0764 P(z 0.58) z 0.2810 P(z > 2.76) = 0.0029 (c) The proper conclusion of the hypothesis test is (i) Fail to reject Họ. There is not sufficient evidence that the populations means are different. (ii) Reject Ho. There is not sufficient evidence that the populations means are different. (iii) Fail to reject Ho. There is sufficient evidence that the populations means are…arrow_forward
- a) Let Y₁,Y2,...,Yn be a random sample taken from a normal distribution with mean, and variance, 9. We intend to test Ho: = 3 versus H₁: =4. Find the sample size, n if Ho is to be rejected for all X≥5.382 with the probability of Type II error, ß = 0.063.arrow_forwardAn ecologist records the hourly number of birds x; (i = 1,2,3,...,40) flying over a wetland. The data summaries are 40 40 Σx, = 1200 and Σx² = 285 000. i=1 i=1 ii Based on past records, the number of the population mean of birds flying over the wetland in an hour is 34. Estimate the probability that the sample mean number of birds for 40 hours (1) is greater than 40, (2) is between 25 and the sample mean.arrow_forward• Exercise 7 If Y1, Y2, . .., Yn denote a random sample from the normal distribution with mean u and variance o2, find the method-of-moments estimators of u and o2.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL