Question

Fill out the table below based on the simulations. How many of the intervals contained the true parameter in each of the different simulation?

Theoretically, what percent of intervals should contain the true mean?

Is there evidence from the simulation that this is approximately the same accuracy rate?

Which of the following simulations represents what we do “in real life”?

# of random samples of size n	1 Sample of size n	10 Samples of size n	100 Samples of size n	1000 Samples of size n
Count that contain the true mean	1	9	91	919
Percent that contain the true mean	1	10%	100%	1000
Percent that don’t contain the true mean	100%	90%	91%	91.9%

Answer 1

In interval of 1 sample of size n

According to given observations the total sample of size n i.e. 1 will contain true mean.so, percent that contains true mean is 100 instead of 1

In interval of 10 sample of size n

9 out of 10 contain true mean so ,there is 90% of sample contains true mean instead of only 10%

In interval of 100 sample of size n

91 out of 100 sample contains true mean so,there is 91% of sample contains true mean instead of 100%

In sample of 1000 of size n

919 sample out of 1000 contains true mean so,there is 91..9% of sample contains true mean

There is no any evidence from the simulation that this is approximately the same accuracy rate as this may change or we can say slightly different due to chance causes.

The simulation that contains the true mean really represent what we do in our real life as our decision totally depends on the percentage of true data or information.