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 0.11 milligrams per liter (mg/L). A random sample of 10 precipitation dates in 2007 results in the following data table.

Data:

0.068 0.084 0.059 0.278 0.117 0.172 0.109 0.218 0.337 0.092

Complete parts (a) through (c) below.

(a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990. H0: μ = 0.11 mg/L H1: μ ≠ 0.11 mg/L

(b) Construct a 99% confidence interval about the sample mean concentration of calcium precipitation. The lower bound is______ . The upper bound is______ . (Round to four decimal places as needed.)

(c)

A. No, because the confidence interval contains 0.11 mg/L.

B. No, because the confidence interval does not contain 0.11 mg/L.

C. Yes, because the confidence interval contains 0.11 mg/L.

D. Yes, because the confidence interval does not contain 0.11mg/L.

Answer 1

a)

H0: μ = 0.11 mg/L H1: μ ≠ 0.11 mg/L.

b)

Sample size = n = 10

Sample mean = = 0.1534

Standard deviation = s = 0.0954

We have to construct 99% confidence interval.

Formula is

Here E is a margin of error.

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

Level of significance = 0.01

tc = 3.250 ( Using t table)

So confidence interval is ( 0.1534 - 0.098 , 0.1534 + 0.098) = > ( 0.0554 , 0.2514)

c)

C. Yes, because the confidence interval contains 0.11 mg/L.