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 0.12 0.12 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. LOADING... Click the icon to view the data table. ​(a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990. Upper H 0 H0​: mu μ equals = 0.12 0.12 ​mg/L Upper H 1 H1​: mu μ not equals ≠ 0.12 0.12 ​mg/L ​(b) Construct a 95 95​% confidence interval about the sample mean concentration of calcium precipitation. The lower bound is nothing . The upper bound is nothing . ​(Round to four decimal places as​ needed.) Enter your answer in the edit fields and then click Check Answer. 1 part remaining Clear All Check Answer Data Table 0.073 0.073 0.084 0.084 0.071 0.071 0.264 0.264 0.128 0.128 0.188 0.188 0.104 0.104 0.218 0.218 0.338 0.338 0.113 0.113

Answer 1

Solution:

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 0.12 milligrams per liter​ (mg/L).

That is :

We have to test if the mean concentration of calcium precipitation has changed since 1990.

Sample size = n = 10

Data Table: 0.073 , 0.084 , 0.071 , 0.264 , 0.128 , 0.188 , 0.104 , 0.218 , 0.338 , 0.113 .

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

mg/L

Vs

mg/L

Part b) Construct a 95​% confidence interval about the sample mean concentration of calcium precipitation.

Since sample size n = 10 is small and population standard deviation is unknown, we use t distribution to Construct a 95​% confidence interval about the sample mean.

Formula:

where

Thus we need to make following table:

x	x^2
0.073	0.005329
0.084	0.007056
0.071	0.005041
0.264	0.069696
0.128	0.016384
0.188	0.035344
0.104	0.010816
0.218	0.047524
0.338	0.114244
0.113	0.012769

and

and t_c is t critical value for c= 95% confidence level

df = n - 1 = 10 - 1 = 9

Two tail area = 1 - c = 1 - 0.95 = 0.05

Look in t table for df = 9 and two tail area = 0.05 and find area.

t_c = 2.262

Thus Margin of Error is:

Thus

The lower bound is :

and

The upper bound is :

Conclusion:

Since 95% confidence interval about the sample mean concentration of calcium precipitation is between ( 0.0931 , 0.2231 )

which include claimed mean 0.12 mg/L , that means population mean is not different from 0.12 mg/L

Thus there is not sufficient evidence to conclude that: the mean concentration of calcium precipitation has changed since 1990.