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 90% confidence?

Answer 1

68

Explanation:

To get the sample size of the population, we will use the formula for calculating the standard error of the mean. This is expressed as;

SE = zσ/√n

z is the z score at 90% confidence

σ is the standard deviation

n is the sample size

SE is the mean weight loss

Given

z = 1.645

σ = 10

SE = 2

Required

sample size n

Substitute into the given equation;

SE = zσ/√n

2 = (1.645)(10)/√n

2 = 16.45/√n

√n = 16.45/2

√n = 8.225

n = (8.225)²

n = 67.650625

Hence the total sample should be about 68