Question

1. As we learned from the previous chapter, the distribution of SAT scores is normal with a m = 500 and a s = 100. If you select a random sample from this population, on average, how much error would you expect between the sample mean and the population mean for each of the following samples?
   1. What do we call “the amount of error you would expect between a sample mean and a population mean”. I gave you a name for that value… what is it?

2. Okay, now answer the question for the following sample sizes:

                             n = 4

                             n = 25

                             n = 100

Answer 1

let X be the random variable which denotes the SAT scores.

It is given that X ~ N( 500, 100²)

Note that, to find the  % confidence interval for sample mean

we have the following statement

So, if = 0.05, we can obtain the 95% confidence interval for sample mean, note that at the right hand side of the inequality inside the probability system is the margin of error.

Infact, confidence interval = sample statistic margin of error,

a) margin of error is the stipulated error between the sample mean and the population mean.

b) note that,

therefore, margin of error = ...........(1)

Putting n=4, 25, 100 respectively, we get.

Margin of error when n=4 is  

when n=25, margin of error =

when n=100, margin of error =

note that, as sample size increases margin of error decreases giving us better estimate for the population mean.