Question

Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipitation in a certain area was .15 milligrams per liter. A random sample of 10 precipitation dates in 2007 results in the following data table.

.077

.087

.077

.243

.125

.185

.132

.212

.328

.103

Construct a 95% confidence level about the sample mean concentration of calcium precipitation.

Does this sample evidence suggest that the calcium concentrations have changed since 1990?

Answer 1

From the data,

sample mean = 0.1569

sample standard deviation s = 0.08347381

standard error of mean = s/ = 0.08347381 / = 0.02639674

Degree of freedom = n-1 = 10-1 = 9

Critical value of t at df = 9 and 95% confidence level is  2.26

95% confidence interval of the mean concentration of calcium precipitation is,

(0.1569 - 2.26 * 0.02639674 ,  0.1569 + 2.26 * 0.02639674)

(0.097 ,  0.217)

Since the 95% confidence interval contains the value of 0.15 milligrams per liter of 1990 level, we can conclude that the calcium concentrations have significantly not changed since 1990.