ISYE-3030-Assignment-3

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Georgia Institute Of Technology *

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4031

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Statistics

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Feb 20, 2024

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docx

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6

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ISYE 3030 Assignment 3 Lokranjan Lakshmikanthan 10/6/2021 Libraries library (tidyverse) Question 8.2.9 Part A Chapter8 = read.csv ( "ch08.csv" ) data = na.omit (Chapter8 $ EX. 8 . 2.9 ) ggplot ( as.data.frame (data), aes ( sample = data)) + stat_qq () + stat_qq_line () The data appears to be approximately normal. The data mostly falls on the linear line shown in the normal probability plot above. The deviations of the data points from the line
are small enough to assume normality however the population variance is not known. Below is the confidence interval made using T-scores. Part B sMean = mean (data) SD = sd (data) n = length (data) t = qt ( 0.975 , n -1 ) TwoSidedError = t * SD / sqrt (n) Upper = sMean + TwoSidedError Lower = sMean - TwoSidedError Upper ## [1] 2282.516 Lower ## [1] 2237.317 The two-sided 95% confidence interval on the mean strength is (2237.317 <= True Mean <= 2282.516) Part C OneSidedError = qt ( 0.95 , n -1 ) * SD / sqrt (n) Lowerz = sMean - OneSidedError Lowerz ## [1] 2241.477 The one-sided lower 95% confidence interval on the mean strength is (2241.477 <= True Mean). The lower bound of the two-sided interval is less than the lower bound for the one sided interval. This is since the alpha of the one-sided interval is larger and results in a lower T-score. The lower T-score reduces the error on the one-sided interval. Question 8.3.3 data2 = as.numeric (Chapter8 $ EX. 8 . 3 . 3.1 [ 2 : 9 ]) ggplot ( as.data.frame (data2), aes ( sample = data2)) + stat_qq () + stat_qq_line ()
Data from the Average Mean Temperature of the 8 sites appears to be normally distributed. The normal probability plot has few extreme deviations from the line making it reasonable to assume a normal distribution. SQU = qchisq ( 0.975 , 7 ) SQL = qchisq ( 0.025 , 7 ) V1 = var (data2) n1 = length (data2) - 1 LowerC = sqrt ((n1 * V1) / SQU) UpperC = sqrt ((n1 * V1) / SQL) LowerC ## [1] 1.402562 UpperC ## [1] 4.317464 By assuming a normal distribution for the data we can arrive at a 95% two-sided confidence interval for the standard deviation over the sites: (1.402562 <= True Standard Deviation <= 4.317464).
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