Sampling and estimation — practice question

The masses of animals from one particular species are assumed to follow a normal distribution with standard deviation $\sigma$ kg. A researcher takes the masses of a random sample of $n$ animals of this species and uses them to construct two confidence intervals ($\alpha\%$ and 90%) for the population mean. The width of the $\alpha\%$ confidence interval is 1.414 times as large as the width of the 90% confidence interval.