Question

Data on fifth-grade test scores (reading and mathematics) for 420 school districts in California yield average score Y = 655.2 and standard deviation sY = 19.1. Construct a 95 % confidence interval for the population mean test scores. Interpret.

Answer 1

The 95 % confidence intervals (653.3 , 657.0) for the population mean test score

Explanation:

Given school districts n = 420

The average score (Population mean) μ = 655.2

and standard deviation σ = 19.1

The 95% of confidence intervals μ± 1.96 σ/√n

The 95% of confidence intervals (μ- 1.96 σ/√n , μ+ 1.96 σ/√n)

The 95% of confidence intervals

( (
`655.2-1.96(19.1)/(√(420) ) , 655.2+1.96(19.1)/(√(420) )`) ,

(655.2-1.826 , 655.2+1.826)

(653.3 , 657.0)

Conclusion:-

The 95 % confidence intervals (653.3 , 657.0) for the population mean test score