b) Suppose that a random variable X has a probability density function given as(2(ß-x)B²0,0 < x

A quantity is said to be pivotal quantity if it's distribution is free from parameter of interest.

Answered: i) Use an appropriate method to show…

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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10. A chemist has developed a new synthetic fiber. To measure the fiber's strength, experiments are performed on ten strands of this fiber to determine the average number of pounds that can be supported by strands of this fiber before breaking. The following breaking-load results (in pounds) were obtained: 3.3 2.2 3.1 2.8 2.6 2.9 3.0 2.4 2.7 3.2 Construct a 95% confidence interval for the mean breaking strength of a strand of this new fiber.
2. A 95% confidence interval for the MEAN recovery time after a certain major surgery is (100, 130) days. a) Find the sample mean used to form the interval. b) Find the margin of error. c) Assume that the population standard deviation is 40. Determine the sample size needed to create the confidence interval (110, 130) with the margin of error you found in part b.
a) Find right side tail for t = 2.447 and sample size 7 b) Find level of confidence interval for t = 2.447 and sample size 7 c) Find level of confidence interval for t = 1.725, sample size 21
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1. In a test of the effectiveness of garlic for lowering cholesterol, 43 subjects were treated with garlic processed tablet form. Cholesterol levels were measured before and after the treatment. The chang (before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 4.2 and a standard devia 19.4. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in redu LDL cholesterol?
2. In a simple random sample of 1200 Americans age 20 and over, 138 of them were found to have Type I diabetes. Round all answers to three decimal places. a) Report a 95% confidence interval for the proportion of all Americans age 20 and over with diabetes. J b) According to the Centers for Disease Control and Prevention, nationally, 10.7% of all Americans age 20 and over have diabetes. Does the confidence interval you found support or refute this claim? Explain.
5. a). What is a fundamental difference between the t statistic and a z-score in terms of variability? b). What value is estimated with a confidence interval using the t statistic?
A random sample of 180 men indicated that 50 were smokers, and a random sample of 150 women surveyed indicated that 39 smoked. Construct a 98% confidence interval for the true difference in proportions of male and female smokers.
The Procrastination Log (PL)…was administered both at intake [pretest to a one-hour individual counseling session on procrastination] and on outtake [posttest]. The PL is the most widely used instrument for assessing difficulties with procrastination. It is a 9-item self-report questionnaire that measures procrastination-related behavior during the past week. 1) Assuming that the distribution of PL scores for the “No attribution group” at “Intake” is normal, between what two scores did approximately the middle 95% of participants lie?- 2) Assuming that the distribution of PL scores for the “No attribution group” at “Outtake” is normal, between what two scores did approximately the middle 99.7% of participants lie? 3) On average, which group showed the greatest improvement from “Intake” to “Outtake”?-
Dr. Maddan's eye drops are supposed to cause significant reduction is eye redness. The following table shows the results of a recent study where a random sample of individuals took part in a placebo controlled study. No Reduction in Redness Reduction in Redness Total Eye Drops 120 220 340 No Eye Drops Total 120 140 260 240 360 600 With 5% level of significance, determine if eye redness reduction is dependent upon taking the eye drops. Provide, a. the Chi-square statistic. b. the critical value or the p-value. c. Your decision on whether or not to reject Ho.

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i) Use an appropriate method to show that W = is a pivotal quantity. ii) Construct a 90% upper confidence limit for ß, using part i) of Question 4 b).