A particular article presents chemical analyses of runoff wa

A particular article presents chemical analyses of runoff water from sawmills in British Columbia. Included were measurements of pH for six water specimens: 5.8, 5.0, 6.5, 5.7, 5.9, 5.3. Assuming these to be a random sample of water specimens from an approximately normal population, find a 95% confidence interval for the mean pH. Round the sample standard deviation to five decimal places and the interval bounds to three decimal places each. The confidence interval is

Solution

sample mean= 5.7
stample standard deviation = 0.517687

The degree of freedom = n-1=6-1=5

Given a=1-0.95=0.05, t(0.025, df=5) =2.57 (from student t table)

So the lower bound is

xbar- t*s/vn = 5.7- 2.57*0.517687/sqrt(6) =5.157

So the upper bound is

xbar + t*s/vn =5.7+ 2.57*0.517687/sqrt(6) =6.243