Question

Base on data from the number of hours that 10 hospital patients slept following the administration of a certain anesthetic, the following 90% confidence interval for the average hours slept following the administration of the anesthetic was produced, (7.77, 9.69). What was the sample standard deviation? (answer to 2 decimal places)

Answer 1

We have

xbar - E = 7.77

xbar + E = 9.69

Solving these equations

E = 0.96

But here E =t​​​​​​a/2*( s/√n)

For a = 0.10 and d.f = n -1 = 9

t​​​​​​a/2 , n-1 = t​​​​​​0.05, 9 = 1.833

sample standard deviation s =( E * √n) / t​​​​​​a/2

s = (0.96*√10)/1.833

Sample standard deviation s = 1.66