Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information.30 2 11 17177 34 132 127Xy=b=ŷ =USE SALTEx = 73; Ey = 592; Ex² = 1,399; Ey² = 73,608; Exy = 9,790(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)x=(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.yy200150XV10050X20015010050200150100505 10 15 20 25769 535200150Vy1005010152030 3525O35510X15 20 25 30 355 1015 20 2530 35O(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)r² =What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)%(d) For a neighborhood with x = 17% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.)crimes per 1000 residents▸

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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 random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.)
1. Assume there are a population size N = 6 with units (2,4,6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (*/) + 10, where si = (x;-1)² is unbiased estimator of the variance of the random sample X 22-1 to the population variance, and X is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.
The population mean will always be the same as the mean of all possible X that can be computed from samples of size 38. O True O False
Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone. x 1,004 975 992 935 971 924 y 40 100 65 145 77 154 Use a calculator to verify that x = 5,801, x2 = 5,613,547, y = 581, y2 = 66,495 and xy = 554,778.Compute r. (Round your answer to four decimal places.)r = As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.Given our value of r, y should tend to remain constant as x increases.Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
1. Of all customers purchasing automatic garage-door openers, 57% purchase a chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model. a. Calculate P(X > 10). b. Calculate P(8
Three randomly selected children are surveyed. The ages of the children are 2, 3, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 2,2 2,3 2,10 3,2 3,3 3,10 10,2 10,3 10,10 a. Find the value of the population variance o². (Round to three decimal places as needed.)
Just need B. These are old practice problems
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 67 70 69 81 65 86 y 51 54 45 56 50 49 Given that ∑x = 438, ∑y = 305, ∑x2 = 32,332, ∑y2 = 15,579, ∑xy = 22,302, and r = 0.226, find the P-value for a test claiming that ρ is greater than zero. 0.25 > P-value > 0.10 0.10 > P-value > 0.05 0.40 > P-value > 0.25 P-value < 0.0005 P-value > 0.40X
A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.9 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value
9
There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable W is the difference between X and Y. That is, W = X - Y. Calculate the mean of W.
If two large random samples are drawn from two populations, each having a mean of $100, the relevant sampling distribution of their difference has a mean of a. 200 b. The Sum of the 2 Sample Means C. 0 D. The difference between the two sample means.

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