Question

There are 255 students this term completing this same assignment. Assuming they calculated the CI correctly, how many students should we expect to have an interval that does not contain the true mean?

Answer 1

Answer:

The number of students we expect to have an interval that does not contain the true mean value is,  $255\times [\alpha\%]$.

Step-by-step explanation:

A [100(1 - α)%] confidence interval for true parameter implies that if 100 confidence intervals are created then [100(1 - α)] of these 100 confidence intervals will consist the true population parameter value.

Here α is the significance level. It is defined as the probability rejecting the claim that the true parameter value is not included in the 100(1 - α)% confidence interval.

It is provided that 255 students create the same confidence interval, correctly.

Then the number of students we expect to have an interval that does not contain the true mean value is,  $255\times [\alpha\%]$

For instance, if the students are creating a 95% confidence interval for mean then the number of students we expect to have an interval that does not contain the true mean will be:

The significance level is:

$Confidence\ level=100(1-\alpha)\\\frac{95}{100}=(1-\alpha)\\\alpha =1-0.95=0.05$

Number of students we expect to have an interval that does not contain the true mean will be: $255\times [\alpha\%]=255\times 0.05=12.75\approx13$

Thus, 13 of the 255 confidence intervals will not consist the true mean value.