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 685 exams in his state. The sample mean for the test is 490.

Find the 90% confidence interval to estimate the mean SAT math score in this state for this year.

(Note: The critical z-value to use, zc, is: 1.645.)

Your answer should be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 490

Population standard deviation =    = 100

Sample size = n = 685

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 100 /  685 )

= 6.285

At 90% confidence interval estimate of the population mean is,

  ± E

490 ± 6.285   

( 483.715, 496.285 )