Question

An Environmentalist is making a survey on the number of households that applies the principles of Waste Management in a certain community. Given the standard deviation of 26, how large a sample must be selected if we want to be 95% confident of finding whether the true mean differs from the sample mean by 1.5 hour?

Answer 1

Based on the information provided, the significance level is $\alpha = 0.05,$ and the critical value for a two-tailed test is $z_c =1.96.$

$$E=z_c\times\dfrac{\sigma}{\sqrt{n}}$$ $$n\ge(\dfrac{z_c\times \sigma}{E})^2$$ $$n\ge(\dfrac{1.96\times 26}{1.5})^2$$

$$n=1155$$