Question

Problem 2

A neurological disease is characterized by gait imbalance. To provide effective treatment, it is important to detect the disease as soon as possible. In an experiment, age at onset of symptoms and age at diagnosis for 18 patients suffering from the disease were recorded for the same patients (in months). The differences in age were observed to be -38.60 months with a sample standard distribution of 23.18. Calculate a lower 95% confidence bound for the population mean of age differences and interpret the answer.

Answer 1

Sol:

Md=-38.60

Sd=23.18

n=18

df=n-1=18-1=17

alpha-0.05

alpha/2=0.05/2=0.025

Tcritical value in excel

=T.INV(0.025,17)

=2.019

95% confidence interval for mean is

Md-T*Sd/Sqrt(n),Md+T*Sd/Sqrt(n)

-38.60-2.019*23.18/sqrt(18),-38.60+2.019*23.18/sqrt(18)

-49.63096,-27.56904

lower 95% confidence bound for the population mean of age differences =-49.63096

we are 95% confident that the true mean  differences in age(age at onset of symptoms and age at diagnosis)lies in between -49.63096 and -27.56904