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A large chain of retail outlets has several stores in each capital city of Australia, including a similar number of stores in each of Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)2 and the variance of monthly profits in Perth is about 1789(k$)2. A comparison of the difference in profits between the two cities indicates that the variance of the monthy difference in profits between these cities is about 1253(k$)². i) Use this information to calculate the covariance of the monthly profits in these two Hence find the correlation (p) between the monthly profits in these two cities. ii) cities.

A large chain of retail outlets has several stores in each capital city of Australia, including a similar number of stores in each of Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)2 and the variance of monthly profits in Perth is about 1789(k$)2. A comparison of the difference in profits between the two cities indicates that the variance of the monthy difference in profits between these cities is about 1253(k$)². i) Use this information to calculate the covariance of the monthly profits in these two Hence find the correlation (p) between the monthly profits in these two cities. ii) cities.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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2 Linear combinations and inference (a) A large chain of retail outlets has several stores in each capital city of Australia, including a similar number of stores in each of Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)² and the variance of monthly profits in Perth is about 1789 (k$)2. A comparison of the difference in profits between the two cities indicates that the variance of the monthy difference in profits between these cities is about 1253(k$)². i) Use this information to calculate the covariance of the monthly profits in these two ii) cities. Hence find the correlation (p) between the monthly profits in these two cities. (b) Quality control staff wish to estimate what proportion p of the resistors made in their factory are being scrapped due to defects. They observe a random sample of n = 750 resistors from the production line and calculate the sample proportion of scrapped resistors to be p = 0.016. Use this information and the statistical tables provided on Canvas to determine an approximate range a such that the sample proportion from a sample of this size will lie within a of p with confidence level 99%, that is, such that Pr(p - p| <a) = 0.99. (c) The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measure- ment system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.) The latest sample of eight measurements gave a sample average concentration (X) of 8.13 mmol/L and a sample standard deviation (s) of 0.16 mmol/L. Use this information and the statistical tables provided on Canvas to carry out the statistical test mentioned above, and report on what evidence (if any) there is to suggest that the mean concentration of the chemical has varied from the desired level.
Transcribed Image Text:2 Linear combinations and inference (a) A large chain of retail outlets has several stores in each capital city of Australia, including a similar number of stores in each of Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)² and the variance of monthly profits in Perth is about 1789 (k$)2. A comparison of the difference in profits between the two cities indicates that the variance of the monthy difference in profits between these cities is about 1253(k$)². i) Use this information to calculate the covariance of the monthly profits in these two ii) cities. Hence find the correlation (p) between the monthly profits in these two cities. (b) Quality control staff wish to estimate what proportion p of the resistors made in their factory are being scrapped due to defects. They observe a random sample of n = 750 resistors from the production line and calculate the sample proportion of scrapped resistors to be p = 0.016. Use this information and the statistical tables provided on Canvas to determine an approximate range a such that the sample proportion from a sample of this size will lie within a of p with confidence level 99%, that is, such that Pr(p - p| <a) = 0.99. (c) The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measure- ment system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.) The latest sample of eight measurements gave a sample average concentration (X) of 8.13 mmol/L and a sample standard deviation (s) of 0.16 mmol/L. Use this information and the statistical tables provided on Canvas to carry out the statistical test mentioned above, and report on what evidence (if any) there is to suggest that the mean concentration of the chemical has varied from the desired level.
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