Question

The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 619 exams in his state. The sample mean for the test is 499.

Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.

(Note: The critical z-value to use, zc, is: 2.576.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 499

Population standard deviation =    = 100

Sample size = n = 619

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 100 /  619 )

= 10.35

At 99% confidence interval estimate of the population mean is,

  ± E

499  ± 10.35   

( 488.65, 509.35 )