ӨA head teacher wishes to estimate a parameter representing the proportion of her year 6pupils who will attain the expected level in their upcoming science test. Two teacherssummarize their beliefs about . Mr. Wilkes decides that a Beta (20, 8) represents hisbeliefs, while Miss Green decides that a Beta(11, 2) represents her beliefs.(a) Calculate the mode and variance for both Mr. Wilkes' and Miss Green's prior beliefsabout 8.(b) Whose prior beliefs are the strongest, Mr. Wilkes' or Miss Green's? Justifyyour answer.(c) The head teacher herself does not believe that any one value of 0 is any morelikely than any other value of 0. Suggest a suitable prior to summarize her beliefs.

(a) For a Beta distribution with parameters α and β, the mode is given by (α - 1) / (α + β - 2) and…

Answered: Ө A head teacher wishes to estimate a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A history instructor has given the same pretest and the same final examination each semester. he is interested in determining if there is a relationship between the scores of the two tests. he computes the linear correlation coefficient and notes that it is 1.15. what does the correlation coefficient value tells the instructor? a. there is a strong positive correlation between the test b. there is a strong negative correlation between the test c. the history instructor has made a computational error d. the correlation is something other than linear
e. Compute the covariance and correlation coefficient r between the right tire pressure. f. How do you know the relationship between pressure in the left and right tires is positive. g. What value would a correlation coefficient (r) be close to if there was no (linear) relationship between the 2 tire pressures?
Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. a. Identify the independent and dependent variables. b. In a sentence, state the null hypothesis being tested. c. Using symbols, state the null and alternative hypotheses. d. Determine the critical region using a one-tailed test with alpha = .05. e .Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). f. State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). g. Based on your analysis, is there a relationship between the drug and attention span?
A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. How would the value of the correlation coefficient, r, change if sodium was plotted on the x-axis and calories plotted on the y-axis? The value of r would increase. The value of r would not change. The value of r would change to –0.83. The value of r could increase or decrease, depending of the strength of the new relationship.
A researcher wanted to find the effect of a special diet on systolic blood pressure. She selected a sample of seven adults and put them on this dietary plan for 3 months. The following table gives the systolic blood pressures (in mm Hg) of these seven adults before and after the com- pletion of this plan. Before After 210 193 180 186 195 186 220 223 231 220 199 183 224 233 Let u be the mean reduction in the systolic blood pressures due to this special dietary plan for the population of all adults. Construct a 95% confidence interval for ud. Assume that the population of paired differences is (approximately) normally distributed.
A police academy has just brought in a batch of new recruits. All recruits are given an aptitude test and a fitness test. Suppose a researcher wants to know if there is a significant difference in aptitude scores based on a recruits’ fitness level. Recruits are ranked on a scale of 1 – 3 for fitness (1 = lowest fitness category, 3 = highest fitness category). Using “ApScore” as your dependent variable and “FitGroup” as your independent variable, conduct a One-Way, Between Subjects, ANOVA, at α = 0.05, to see if there is a significant difference on the aptitude test between fitness groups. Identify the correct symbolic notation for the alternative hypothesis. A. H0: µ1 = µ2 B. HA: µ1 ≠ µ2 ≠ µ3 C. H0: µ1 = µ2 = µ3 D. HA: µ1 ≠ µ2
A researcher computes the correlation coefficient r= 0.4212 for an explanatory and response variable. What proportion of the changes in the response variables value is accounted for by the change in the explanatory variable's value? Give your answer to four decimal places.

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