Question

# There are two elementary schools in Caleb's community. Third graders in both schools recently took the...

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.

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)

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