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 0.15 milligrams per liter (mg/L). A random sample of 10 precipitation dates in 2007 results in the following data table. Complete parts (a) through (c) below.

(a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990.

(b) Construct a 99% confidence interval about the sample mean concentration of calcium precipitation.

(c) Does the sample evidence suggest that calcium concentrations have changed since 1990?

Data Table:

0.073
0.088
0.067
0.239
0.128
0.181
0.104
0.207
0.331
0.092

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 0.15
Alternative Hypothesis, Ha: μ ≠ 0.15

b)

sample mean, xbar = 0.151
sample standard deviation, s = 0.0866
sample size, n = 10
degrees of freedom, df = n - 1 = 9

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.25

ME = tc * s/sqrt(n)
ME = 3.25 * 0.0866/sqrt(10)
ME = 0.089

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (0.151 - 3.25 * 0.0866/sqrt(10) , 0.151 + 3.25 * 0.0866/sqrt(10))
CI = (0.06 , 0.24)

c)

No, the sample evidence does not suggest that calcium concentrations have changed since 1990

as the confidenc einterval contain s0.15