Concept explainers
Refer to Exercises 1.129 and 1.130. S2 and S′2 are two estimators for σ2 that are of the form
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Mathematical Statistics with Applications
- Assuming all other factors are held constant ,if the df value for a two tailed t test with x=.05 were increased from df=6 to df=20,what would happen to the critical values for t? the critical values would further from t=0 the crtical values would move closer to t=0 the crtical values would not change this is impossible to determinearrow_forwardSee the attached image for the introduction. In terms of variables xi and parameters βi, write the null and alternative hypotheses for testing whether, after including Price/Square Feet(x2) in the model already, the further incorporation of the other 2 explanatory variables (x1, x3) adds any useful information for explaining pricey. Also, give the value of the F statistic and its degrees of freedom (df).arrow_forwardSuppose we consider the following model: Xt2 = b0 + b1X2t-1 + ut The estimation of the model provided the following: Xt2 = 0.00043 + 0.23036X2t-1 t = (7.71) (4.97) R2 = 0.0531 d = 1.9933 where Xt2 is as defined before. Given a p value for b1 of .0001 what do conclude about the significance of the model?arrow_forward
- Given the Data:Test the hypothesis that p(rho)xy is not equal to 0 at the 0.05 level of significance.arrow_forwardSolve An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05. 1.)This problem is a test on what population parameter? a.Variance/ Standard Deviation b.Mean c.Population Proportion d.None of the above 2.)What is the null and alternative 3 points hypothesis? a.Ho / (theta = 22.5) , Ha: (0 # 22.5) b.Ho / (theta > 22.5) , Ha: (0 # 22.5) c.Ho / (theta < 22.5) , Ha: (theta >= 22.5) d.None of the above 3.)What are the Significance level 3 points and type of test? alpha = 0.05 two-tailed alpha = 0.95 two-tailed alpha = 0.95 one-tailed None of the above 4.)What standardized test statistic will…arrow_forwardChoose the letter of the correct answer. 1. In one tailed test, in which critical values below will the computed z of 2.312 falls in the non rejection region? A. 1.383 B. 1.533 C. 2.228 D. 2.354arrow_forward
- The test statistic of z=−2.60 is obtained when testing the claim that p<0.63. a. Using a significance level of α=0.01, find the critical value(s). b. Should we reject H0 or should we fail to reject H0?arrow_forwardL12Q5.At 10% level of significance, the critical value(s) of z to test H0: μ1= μ2; against Ha: μ1 ≠ μ2 is/arearrow_forwardIf X is b(100,0.1), how do you find the value of P(12 < X < 14) using the normal approximation and the Poisson approximationarrow_forward
- For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.3, y=6.0, r=−0.228, P-value=0.111, and y=7.81−0.280x. Find the best predicted value of y(attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=5. Use a 0.10 significance level. The best predicted value of ywhen x=5 is nothing. (Round to one decimal place as needed.)arrow_forwardYou are conducting quality control for a company that manufactures LED displays. The factory you are assessing is supposed to have a manufacturing defect rate of 1 in 100 LED displays. As part of your assessment, you want to verify this defect rate by analyzing a random sample of LED displays. You are planning to randomly sample 1500 displays from this factory and observe how many of them contain manufacturing defects. Let Zi be equal to 1 if the i’th display has a defect and 0 otherwise, for i = 1,...,1500. (a) What is the statistic that you will use to estimate the defect rate for this factory? How do you compute it using Z1, Z2, . . . , Z1500? (b) Assuming that the true defect rate for this factory is in fact 1 in 100 displays, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal…arrow_forwardf X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman