Question

There are two elementary schools in Caleb's community. Third graders in both schools recently took the same standardized exam. A random sample of 45 third graders from the first school has a mean score of 75. A random sample of 39 third graders from the second school has a mean score of 78. Assume the population standard deviations of the third graders' scores are known to be 10 for the first school and 5 for the second school. Construct and interpret a 95% confidence interval for the true difference between the mean exam scores for the two schools.

Answer 1

Solution:

point estimate =    - = 75 - 78  = -3

c = 95% = 0.95

= 1 - c = 1 - 0.95 = 0.05

/2 = 0.025

= 2.576 ..(Using z table)

Margin of error =   

=  

= 3.3165

Confidence interval is

point estimate margin of error

-3 3.3165

(-3 - 3.3165, -3 + 3.3165)

(-6.3165 , 0.3165)