Yield of potato resulting from use of different fertilizer (A, B, C, D, E) from CRD experiment with 5 (r) replications and 5 (t) treatments. Yield of potato, kg/plot Treatment II II IV V TI 18 19 17 15 T2 10 18 19 18 10 T3 14 16 14 15 18 T4 14 15 13 15 T5 18 17 10 18
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- q14Germination of a seed commences with the uptake of water and is completed with the appearance of the embryo, in most species radical first, through the surrounding structures. Table 1 gives data regarding germination rates for treated and untreated seeds. (a) (b) Table 1: Germination rates for treated and untreated seeds Germinated Not Germinated 85 120 At 1% significance level, is the germination rate the same for the treated and the untreated seed? (c) Treated Untreated 15 30 State a suitable null and alternative hypotheses for the problem. Test the hypotheses in part (a) by using x² test. Write your conclusion.Process 1 Process 2 Process 3 60 45 50 58 40 52 55 35 56 62 34 47 68 52 48 52 49 52 64 48 51 66 39 50 One-way ANOVA: Process 1, Process 2, Process 3 Source DF ss MS F P Treatment 2 1282.8 Error 21 578.9 Total 23 1861.7 A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appears above. The F-statistic value is F = 27.57. O F = 2.215. O F = 23.267. F = 3.22.
- 1. Is this null hypothesis always testable? Why or why not? 2. Consider the case that this null hypothesis is testable. Construct a statistical test and its rejection region for H0 .X X zy Section 5.4- QNT/275T: Statistics x + 598163/chapter/5/section/4 for Decision Making home > nce between two population means 4.1: Hypothesis test for the difference between two population means. Jump to level 1 A clinical researcher performs a clinical trial on 14 patients to determine whether a drug treatment has an effect on serum glucose. The sample mean glucose of the patients before and after the treatment are summarized in the following table. The sample standard deviation of the differences was 8. Before treatment What is the test statistic? Ex: 0.123 Check What type of hypothesis test should be performed? Select Select Left-tailed z-test Paired t-test Two-tailed z-test Unpaired t-test Next After treatment 75 Sample mean glucose (mg/dL) What is the number of degrees of freedom? Ex: 25 Does sufficient evidence exist to support the claim that the drug treatment has an effect on serum glucose at the a = 0.05 significance level? Select 81 MESA 81101 2 hp 3 IConsider the linear model y=B,+B,x,+B,x,,+B,x+B,+u, You estimate the model y =B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3" 3i 41 The LM statistic +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say O 0.17 O 0.175714 0.177203
- Find the z-score that defines α=0 .05 and α=.01 critical regions for a one-tail test? 8. Find the z-score that defines α=0 .05 and α=.01 critical regions for a two-tail test?Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 6 pairs, with height measured in inches, simulated from the distribution specified by Pearson. Father's Son's height height 69.3 71.4 66.7 68.8 70.7 71.0 65.7 70.9 72.4 69.1 65.4 66.0 Send data to Excel The least-squares regression line y = bo+b,x=50.5230+0.2781x and E (x- x) =41.2733 are known for this data. Use the critical value method to test H:B,=0 versus H, : B,0. Can you conclude that the father's height is useful in predicting the son's height? Use the a=0.01 level of significance. Part: 0 / 4 App Store Part 1 of 4 DEC ... MacBook AirChapter 9: Hypothesis X Chapter 9 Test Chapter 9: Hypothesis X Chapter 9: Hypothesis : XOL 8 /24330/assignments/654472?module_item_id=1905251 Translate A school reports that 83% of its graduates get jobs within one year. You take a random sample of 51 graduates, of whom 38 got a job within one year. Is this enough evidence to show that a significantly smaller percent of graduates get jobs than advertised by the school? (Use a=0.01) 1. For this study, we should use Select an answWer 2. The null and alternative hypotheses would be: Ho:? Select an answer v (please enter a decimal) H: ? Select an answer v (Please enter a decimal) 3. The test statistic (please show your answer to 3 decimal places.) %3D 4. The p-value = (Please show your answer to 4 decimal places.) 5. The p-value is ? v a 6. Based on this, we should Select an answer v the null hypothesis. 7. As such, the final conclusion is that O The sample data suggest that the population proportion is not significantly smaller than 83%…
- 3. The following figure shows the Excel output of a least square multiple linear regression for the scores in a test (variable Y) with Hours (X1, the number of hours spent reviewing) and Prep Exam (X2, the number of exams to take) as independent variables. SUMMARY OUTPUT Regression Statisties Multiple R R Square Adjusted R Square 0.857 0.734 0.703 Standard Error 5.366 Observations 20 ANOVA df Significance F 23.46 MS Regression 1350.76 675.38 0.00 Residual 17 489.44 28.79 Total 19 1840.20 Coefficients Standord Error tStat Pvalue 67.67 Lower 95N Upper 95N Intercept 2.82 24.03 0.00 61.73 73.61 hours 5.56 0.90 6,18 0.00 3.66 7.45 prep exams -0.60 0.91 0.66 052 -2.53 133 a. What is the value of r? What is the practical meaning of this value? b. What is the coefficient of Hours? Interpret this value. c. What is the coefficient of Prep Exam? Interpret this value.Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…Let yit denote the outcome of a random variable for the i-th individual at time and let Xit denote a covariate measure on the i-th individual at time t, t, i = 1, ..., n, t = 1,..., T. The data could be modeled using the simple linear regression model: Yit = Bo + B₁xt + Eit, Eit~N(0, t) a) Explain why using this approach may be inappropriate. b) Write a mathematical expression of the random intercept model and the random coefficients models as alternatives to this model. c) Provide an expression for the proportion of variance attributable to each of the variance components in the random coefficients models. d) Write out an expression for the likelihood, priors and posterior for the model in part (c) e) Write out a WinBUGS code for this problem.