Question

Data on fifth-grade test scores (reading and mathematics) for 412 school districts in California yield Y

ˉ
=659.1 and standard deviation s Y
​
=19.9. The 95% confidence interval for the mean test score in the population is । 1. (Round your responses to two decimal places.)

Answer 1

The confidence interval is (657.18, 661.02)

or , CI = 659.1 ± 1.922

Explanation:

We have to ind the 95% confidence interval,

Mean = Y = 659.1

Standard Deviation = s(Y) = 19.9

Confidence level = 95%

Alpha value = (1 - 0.95)/2

Alpha value = 0.025

So,

This gives a z value of,

z = - 1.96

Now, there are 412 districts so, n = 412

so,

The upper limit is,

Upper limit = UL = Y + z(s(Y))/sqrt(n)

`UL = Upper limit = Y + z(s(Y))/√(n)\\UL = 659.1 + (1.96)(19.9)/|sqrt(412)\\UL = 661.02`

Lower limit is,

LL = Y - z(s(Y))/sqrt(n)

`LL = 659.1 - (1.96)(19.9)/√(412)\\LL = 657.18`

Hence the confidence interval is (657.18, 661.02)