Question

A large restaurant chain is curious what proportion of their customers in a given day are new customers. They

Answer 1

Answer:

It is a false statement

The correct statement is -The margin of error from the smaller sample will be $\sqrt{2}$  times the margin of error from the larger sample.

Step-by-step explanation:

P.S - The exact question is -

Given - A large restaurant chain is curious what proportion of their

            customers in a given day are new customers. They  are thinking  

            of taking a sample of either n = 50 or nº= 100 customers and

            building a one-sample z interval for  a proportion using the data

            from the sample.

To find - The margin of error from the smaller sample will be 2 times

               the margin of error from the larger sample.

Proof -

We know that

E ∝ $\frac{1}{\sqrt{n} }$

For smaller margin, E₁ = $\frac{1}{\sqrt{50} }$

For larger margin , E₂ = $\frac{1}{\sqrt{100} }$

Now,

$\frac{E_{1} }{E_{2} } = \frac{\sqrt{100} }{\sqrt{50} } = \sqrt{\frac{100}{50} } = \sqrt{2}$

⇒E₁ = $\sqrt{2}$ E₂

⇒The margin of error from the smaller sample will be $\sqrt{2}$  times the margin of error from the larger sample.

So,

It is a false statement.