(a) In each Australian capital city, a large retail chain has several stores, including in 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 monthly difference in profits between these cities is about 1253(k$)^2 . (i) Calculate the covariance between the two cities' monthly profits using this information. (ii) Find the correlation (ρ) between the monthly profits in these two cities.
(a) In each Australian capital city, a large retail chain has several stores, including in Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)^2 and the variance of monthly profits in Perth is about 1789(k$)^2 . A comparison of the difference in profits between the two cities indicates that the variance of the monthly difference in profits between these cities is about 1253(k$)^2 .
(i) Calculate the
(ii) Find the
(b) Quality control staff wish to estimate what proportion p of the resistors made in their factory are scrapped due to defects. Based on a random sample of n = 750 resistors from the production line, they calculate the scrapped resistor proportion to be ˆp = 0.016. Use this information to determine an approximate
(c) Chemical concentrations in processing plants are periodically monitored to ensure that they remain near the desired level of 8.25 mmol/L. Multiple samples are taken over a short period of time and the resulting measurements are used to perform a formal statistical analysis due to the variability in the measurement system. You can assume that the measurements are
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