Question

Suppose that you take$500$ simple random samples from a population and that, for each sample, you obtain a $90\%$confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown parameter?

Short answer

There are approximately $50$confidence intervals that will not contain the value of the unknown parameter.

Step-by-step solution

The given information:

The simple random samples are$500.$

Simplification

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

$$\begin{gathered} 90\%of500=\frac{90}{100}\times 500 \\ =90\times 5 \\ =450 \end{gathered}$$

$$\begin{gathered} 90\%of500=\frac{90}{100}\times 500 \\ =90\times 5 \\ =450. \end{gathered}$$

Therefore, approximately $450$confidence intervals are there which will contain the value of the unknown parameter.

The required approximate confidence intervals which will contain the unknown parameter are-$$\begin{gathered} 500-450 \\ =50. \end{gathered}$$

Thus, approximately 50 of the confidence intervals will not contain the value of the unknown parameter.