Q 8.5. - Elementary Statistics

Question

Suppose that you take $1000$ simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?

Step-by-Step Solution

Answer

There are approximately $950$confidence intervals that will contain the value of the unknown parameter.

Step 1 : Given informataion

The simple random samples are: $1000.$

The confidence interval for unknown parameter is: $95\%.$

Step 2: Simplification

We will find the confidence intervals that will contain the unknown parameter's value.

$$\begin{gathered} 95\% of 1000= \frac{95}{100}\times 1000 \\ = 95\times 10 \\ =950. \end{gathered}$$

Therefore, approximately $950$ confidence intervals are there which will contain the value of the unknown parameter.