Exercise 3Consider a pair of random variables (X, Y) with unknown distribution. Assume thedifference D = X – Y is normal with D~ N(D, o). Suppose we are given the followingsample data for (X, Y)²:(16.9, 20.5)(14.6, 21)(23.6, 29.2) (16.2, 22.8) (23.1, 28.2)(22.8, 26.6) (12.7, 17.1) (18.1, 24)Compute a 95% confidence interval of μp¹For comparison, the actual value is μ = 11.7.2For comparison, the actual value is µp = -5.3.(26, 29.9)(22.5, 28.3)(17.3, 22.4)

To compute the confidence interval of μD, we need to estimate μD and the standard error of the…

Answered: Consider a pair of random variables…

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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An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.0153 (fluid ounces) 2. If the variance of fill volume exceeds 0.01 (fluid ounces)2, an unacceptable proportion of bottles will be underfilled or overfilled. Using a level of significance of 0.05, and assuming that fill volume has a normal distribution, answer the following questions. If χ2critical = 30.14, is there evidence in the sample data to suggest that the manufacturer has a problem with underfilled or overfilled bottles?
The score on a standardized test for a certain year is modeled using the normal distribution shown below. The mean of the distribution is 56.7 points and the standard deviation is 4.8 points. In the figure, V is a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) v 68% 95% 99.7% 40 45 50 55 O 60 65 | 70 75 Test score
The two data sets in the table below are dependent random samples. The population of (x - y) differences is approximately normally distributed. A claim is made that the mean difference (x - y) is less than 29.3. X y DII For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t=" before your answers. Round each of your answers to 3 places after the decimal point. (a) Calculate the value of the test statistic used in this test. Test statistic's value = -2.760 61 71 58 48 38 41 (b) Use your calculator to find the P-value of this test. P-value $ 4 44 48 66 43 32 30 29 33 (c) Use your calculator to find the critical value(s) used to test this claim at the 0.07 significance level. If there are two critical values, then list them both with a comma between them. Critical value(s) = -1.700 (d) What is the correct conclusion of this hypothesis test at the 0.07 significance level? O There is sufficient evidence to support the claim that the mean…
I need the answer as soon as possible
Let X 1 , … , X n be identically and independently distributed with population mean 9.3 and standard deviation 1.400. Let xbar be the sample mean, xbar = 1 n ∑ i = 1 n X i. Suppose n = 14. What is the mean squared error (MSE) of 0.742*xbar as an estimator for the population mean?
You have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: • Ho: data follows a N(2, 4²) • HÃ: data follows a N(µ, 4²) where µ ‡ 2. Test statistic: standardized sample mean z. Significance level set to a = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA.
Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the variance (S2) = 9. Z = %3D O 2 -2 .67 -.67
A population of v alues has a normal distribution with μ=48.2 and σ=93.1You intend to draw a random sample of size n=232. Find the value separating the bottom 89% values from the top 11% values. Find the sample mean separating the bottom 89% sample means from the top 11% sample means.
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…
The average size of a farm in Pekan I is 185 acres. The average size of a farm in Pekan II is 100 acre. Assume that the data were obtained from two samples with standard deviations of 38 acres and 12 acres, and sample size of 8 and 9 respectively. Can it be concluded at α = 0.05 that the average size of the farms in Pekan I and Pekan II are different? (Assume equal variances)
Suppose we have the short hand info on a Normal Distribution as N(10,25). What is the population mean of the distribution and what is the population standard deviation? μ = σ =

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