3 - Graded Week 6 Homework-Mark Kasule

Student: Mark Kasule Date: 03/23/24 Instructor: Petal Sumner Course: STAT 200 6961 Introduction to Statistics (1) Assignment: Go - Graded Week 6 Homework Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of and . In general, what does represent? d s d μ d Temperature ( ° F) at 8 AM 99.3 99.9 98.2 98.8 98.1 Temperature ( ° F) at 12 AM 100.4 100.5 98.2 98.0 98.4 For matched pairs, the mean value is the mean value of the differences d for the paired sample data between the first and second values in the pair. d Find the paired differences by subtracting the temperatures at 12 AM from the corresponding temperatures at 8 AM. Temperature ( ° F) at 8 AM 99.3 99.9 98.2 98.8 98.1 Temperature ( ° F) at 12 AM 100.4 100.5 98.2 98.0 98.4 Difference − 1.1 − 0.6 0.0 0.8 − 0.3 Add to find the sum of the differences. d ∑ = − 1.1 − 0.6 − 0.0 + 0.8 − 0.3 = − 1.2 There are n 5 matched pairs in the data set. = Calculate the mean . d d = − 1.2 5 = F − 0.24 ° For matched pairs, the value is the standard deviation of the differences d for the paired sample data between the first and second values in the pair. Use the formula below to calculate the standard deviation. s d s d = ∑ d − d 2 n − 1 First find the deviation from the mean for each difference. d = − 0.24 d − 1.1 − 0.6 0.0 0.8 − 0.3 d − d − 0.86 − 0.36 0.24 1.04 − 0.06 Calculate the squared deviations. d − 1.1 − 0.6 0.0 0.8 − 0.3 d − d − 0.86 − 0.36 0.24 1.04 − 0.06 d − d 2 0.7396 0.1296 0.0576 1.0816 0.0036 Add to find the sum of the squared deviations. ∑ d − d 2 = 0.7396 + 0.1296 + 0.0576 + 1.0816 + 0.0036 = 2.012 Substitute the sum of squared deviations and the number of matched pairs into the formula for the standard deviation and simplify, rounding to two decimal places. s d = 2.012 5 − 1 = F 0.71 ° Thus, the mean difference is F, and the standard deviation of the differences is F. d − 0.24 ° s d 0.71 ° Go - Graded Week 6 Homework-Mark Kasule https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1 of 2 3/23/24, 3:06 AM