A sample of 8 people were taken to see at what age (in years) the prefrontal cor

Question

A sample of 8 people were taken to see at what age (in years) the prefrontal cortex of the brain was completely developed. The sample mean was 24.6 and the sample standard deviation was 3.8. Construct a 95% confidence interval for the population mean age at which the prefrontal cortex of the brain was completely developed. Please Show your work.
I don't know how to do it but the answer is 21.43 < µ < 27.77
A sample of 8 people were taken to see at what age (in years) the prefrontal cortex of the brain was completely developed. The sample mean was 24.6 and the sample standard deviation was 3.8. Construct a 95% confidence interval for the population mean age at which the prefrontal cortex of the brain was completely developed. Please Show your work.
I don't know how to do it but the answer is 21.43 < µ < 27.77

I don't know how to do it but the answer is 21.43 < µ < 27.77
I don't know how to do it but the answer is 21.43 < µ < 27.77

Explanation / Answer

here alpha=0.05, n=8, sd=3.8, mean=24.6

(1-alpha)*100% confidence interval for population mean=mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=mean±t(0.05/2, n-1)*sd/sqrt(n)=24.6±t(0.05/2,7)*3.8/sqrt(8)

=24.6±2.36*3.8/sqrt(8)=24.6±3.17=(21.43,27.77)

so population mean will lies between 21.43 < µ < 27.77

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