Question 21The empirical rule can be broken down into three parts:1. 68% of the data falls within the first standard deviation from the mean.2. 95% falls within two standard deviations3. 99.7% falls within three standard deviations.A) True(B) False

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Answered: Question 21 The empirical rule can be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An investigation of the relationship between traffic flow (measured in cars per day) and lead content (measured in micrograms per gram of dry weight) in the bark of trees near the highway yielded the following summary statistics: Sample Mean Sample Standard Deviation Lead Content (micrograms per gram dry weight) 680 240 Traffic Flow (cars / day) 1750 800 The correlation between lead content and traffic flow was found to be r = 0.6 and a scatterplot showed the form to be linear. Based on context, which is the X-variable and which is the Y-variable? Group of answer choices X-variable Y-variable
(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573. Find the mean and the standard deviation of these z-scores. mean standard deviation (b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are z2 ≈ −1.459, z6 ≈ −0.973, z12 ≈ −0.243, z17 ≈ 0.365, z22 ≈ 0.973, and z25 ≈ 1.337. Find the mean and the standard deviation of these z-scores. mean standard deviation (c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data. The mean of the z-scores is always 1, and their standard deviation is 0. The mean of the z-scores is always 1 more than the standard deviation. The mean and standard deviation of z-scores are never the same.…
A new Economic / Social Conservatism Scale has scores between 0 and 30 (0 being extreme liberal, 30 being extreme conservative). The mean score is 21 and standard deviation of scores is 5. You want to convert the original scale (call it X) to a new scale (call it Y) that has scores between 0 and 100. What is the correlation of X and Y?
One year the ACT had a mean score of 22.7 and a standard deviation of 4.1. minutes. (a)Calculate the z-score of an ACT score of 25. Interpret it using a complete sentence. B. What ACT score is 1.5 standard deviations above the mean? What can you say about this consumption
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The weekly expenditure on groceries of a random sample of 100 family households was recorded. It was estimated that the mean expenditure was approximately $240. With rising interest rates and petrol prices, it was anticipated that grocery expenditure might decrease. Which hypothesis test would you use to test this claim? 1.One tailed, one sample t-test 2.Two tailed, one sample t-test 3.One tailed, z-test 4.One-tailed Paired Samples t-test 5.Chi Square
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Lecture(10.8): The Peabody Picture Vocabulary Test has a standard score mean of 100 and a standard deviation of 15. You tested a class of grade 2 students wonderinf if these scores would be different from the population. After testing this hypotheses you decided to continue looking at this data to determine if there are any group differences based on birth order. You group the children the on whether they are the oldest chlid, middle child, or the youngest child. Here is the data based on grouped information. Oldest child: 87 84 98 104 106 91 96 92 Middle child: 65 74 62 60 73 64 71 78 Youngest child: 115 84 85 83 95 94 108 102 89 Test the hypotheses at (alpha=0.05) level of signifance using the 5 step procedure.Make sure to clearly state the null and alternative hypotheses.Round your answer to 2 decimal. You are encouraged to use the following table to help you…
While reading a published research report, you encounter the following statements. For each, identify the N, the procedure performed and the outcome, the relationship, and the type of error possibly being made. (a) “When we examined the perceptual skills data, the mean of 55 for the sample of adolescents differed significantly from the population mean of 70 for adults, t(45) = 3.76, p < .01.” (b) “The correlation between personality type and emotionality, however, was not significantly different from zero, with r(25) = +.42, p > .05.”
Determine if the following statements are true or false. a. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from the same population. Then, Mike’s sample mean will be closer to the true population mean than Jane’s sample. b. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from a population with mean and standard deviation 2. Then, the sample mean from Mike’s sample is more likely to be close to the true mean than the sample mean from Jane’s sample. That is, the probability that X is between 90% and 110% of mean is higher for Mike’s sample than for Jane’s sample.
You are given the following information: sample mean is equal to 103.55, population standard deviation is equal to 14.88, sample size is equal to 111 and the national average is equal to 109. What would be the value of z-observed?

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Question 21 The empirical rule can be broken down into three parts: 1.68% of the data falls within the first standard deviation from the mean. 2.95% falls within two standard deviations 3. 99.7% falls within three standard deviations. (A) True (B) False