Question

A researcher in the West Coast of the US wants to estimate the amount of newly discovered antibody in human blood. His research funds will only let him obtain blood samples from a random sample of 41 people, so he decides to construct a 95% confidence interval to estimate the mean antibody level in the population. Another researcher on the East Coast of the US is researching the same antibody, but has more research funding and is able to obtain blood samples from a random sample of 121 people. The East Coast researcher also creates a 95% confidence interval for the population mean. How will their confidence intervals compare?

Answer 1

The East Coast confidence interval will be more precise, since the sample is larger.

Explanation:

The margin of a confidence interval is given by the following formula:

`M = z(\sigma)/(√(n))`

In which z is the critical value related to the confidence level,
`\sigma` is the standard deviation of the population and n is the size of the sample.

The larger n is, the lesser the margin of error is, that means that we have a more precise interval.

In this problem:

West Coast: 41 people

East Coast: 121 people

Both 95% confidence interval, so same z. Both about the amount of newly discovered antibody in human blood, so the standard deviation of the population will be the same.

The East Coast has a larger sample. So

The East Coast confidence interval will be more precise, since the sample is larger.