DOC-202505... .archFE Qu... X nment B... X A AQ 2 N CONFIDENTIAL QUESTION 1 [13 MARKS] 24251/BUM2413 In a chemical plant, a plant engineer is focused on assessing the measurements taken by two new operators: Operator A and Operator B. The goal is to evaluate whether the measurements from both operators are consistent, which is crucial for ensuring quality control in chemical processing operations. To achieve this, he has instructed both operators to measure the concentration of two separate chemical samples drawn from the same batch. The Microsoft Excel output based on the recorded sample measurements (in mol/g) for the two operators is presented in Figure 1. t-Test: Two-Sample Assuming Equal Variances Operator A Operator B Mean 10.4200 10.0300 Variance 2.2307 3.9379 Observations 10 10 Pooled Variance 3.0843 Hypothesized Mean Difference 0 df 18 t Stat 0.4966 P(T<=t) one-tail 0.3128 t Critical one-tail 1.3304 P(T<=t) two-tail t Critical two-tail 0.6255 1.7341 Figure 1 Assuming that each sample follows a normal distribution, i) demonstrate that both populations variances are the same based on the sample data at a = 0.1. ii) [8 Marks] [CO2, PO3, C4] investigate whether significant differences exist in population means based on the sample measurements collected from these two operators, utilizing the P-value approach at 10% level of significance. [5 Marks] [CO2, PO3, C4] 2 G A A OB CONFIDENTIAL QUESTION 2 [7 MARKS] 24251/BUM2413 A student claimed that the population variance of cholesterol levels for adult males in a community is 5000. To study potential health risks, she randomly selected 25 men from the community and measured their cholesterol levels in a blood lab. The analysis revealed that the random sample followed a normal distribution, with a 98% confidence interval for the population variance lies between 1762.0586 and 6975.9063. Based on this information, i) conduct an appropriate hypothesis test to evaluate the student's claim regarding the population variance of cholesterol levels. ii) [5 Marks] [CO2, PO3, C4] assess whether a similar conclusion can be drawn from the given confidence interval if the student adjusts the confidence level to 80%, resulting in an interval between 2281.3713 and 4836.4830. State your reason. [2 Marks] [C02, PO3, C3]

DOC-202505... .archFE Qu... X nment B... X A AQ 2 N CONFIDENTIAL QUESTION 1 [13 MARKS] 24251/BUM2413 In a chemical plant, a plant engineer is focused on assessing the measurements taken by two new operators: Operator A and Operator B. The goal is to evaluate whether the measurements from both operators are consistent, which is crucial for ensuring quality control in chemical processing operations. To achieve this, he has instructed both operators to measure the concentration of two separate chemical samples drawn from the same batch. The Microsoft Excel output based on the recorded sample measurements (in mol/g) for the two operators is presented in Figure 1. t-Test: Two-Sample Assuming Equal Variances Operator A Operator B Mean 10.4200 10.0300 Variance 2.2307 3.9379 Observations 10 10 Pooled Variance 3.0843 Hypothesized Mean Difference 0 df 18 t Stat 0.4966 P(T<=t) one-tail 0.3128 t Critical one-tail 1.3304 P(T<=t) two-tail t Critical two-tail 0.6255 1.7341 Figure 1 Assuming that each sample follows a normal distribution, i) demonstrate that both populations variances are the same based on the sample data at a = 0.1. ii) [8 Marks] [CO2, PO3, C4] investigate whether significant differences exist in population means based on the sample measurements collected from these two operators, utilizing the P-value approach at 10% level of significance. [5 Marks] [CO2, PO3, C4] 2 G A A OB CONFIDENTIAL QUESTION 2 [7 MARKS] 24251/BUM2413 A student claimed that the population variance of cholesterol levels for adult males in a community is 5000. To study potential health risks, she randomly selected 25 men from the community and measured their cholesterol levels in a blood lab. The analysis revealed that the random sample followed a normal distribution, with a 98% confidence interval for the population variance lies between 1762.0586 and 6975.9063. Based on this information, i) conduct an appropriate hypothesis test to evaluate the student's claim regarding the population variance of cholesterol levels. ii) [5 Marks] [CO2, PO3, C4] assess whether a similar conclusion can be drawn from the given confidence interval if the student adjusts the confidence level to 80%, resulting in an interval between 2281.3713 and 4836.4830. State your reason. [2 Marks] [C02, PO3, C3]

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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