Answer to Question #215433 in Statistics and Probability for ton

Question

A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds, with a 90% confidence?

Answer 1

The critical value for $\alpha=0.1$ is $z_c=z_{1-\alpha/2}=1.6449$

$$SE=z_c\cdot\dfrac{\sigma}{\sqrt{n}}$$

Given $\sigma=10, SE=2$

$$1.6449\cdot\dfrac{10}{\sqrt{n}}\leq2$$

$$n\geq(1.6449\cdot\dfrac{10}{2})^2$$

$$n\geq68$$

The total sample should be at least 68.