Answer to Question #138164 in Statistics and Probability for Susan Gerea

Question

7. Ecologists have a long advocated recycling newspaper as a way of saving trees and reducing landfills. In recent years, a number of companies have gone into the business of collecting used newspapers from households and recycling them. A financial analyst for one such company has recently calculated that the firm would make a profit if the mean weekly newspaper collection from each household exceeded 1 kg. In a study to determine the feasibility of a recycling plant, a random sample of 100 households showed that the mean and the sample standard deviation of the weekly weight of newspapers discarded for recycling are (mean =1.1kg and SD=0.35Kg). Do these data provide sufficient evidence at the 1% significance level to allow the analyst to conclude that a recycling plant would be profitable? [Define your parameter and show all 6 steps procedure] (10 marks)

Answer 1

$H_0: \mu\leq1\\ H_1:\mu > 1\\ \alpha =0.01\implies Z_{α}=Z_{0.01}=2.326,\\ Z=\frac{\bar x-\mu_0}{\frac{\sigma}{\sqrt n}}\\ Z=\frac{1.1-1}{\frac{0.35}{\sqrt {100}}}=2.857\\ \text{the rejection region} :\;z>2.326\\ \text{The decision is to reject}:\; H_0\\ \text{this means that the analyst can conclude that }\\ \text{ a recycling plant would be profitable if the mean }\\ \text{ weekly newspaper collection }\\ \text{from each household exceeded 1 kg.}$