Question

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Calcium is essential to tree growth because it promotes the formation of wood and maintains cell...

Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipatation in a certain area was 0.12 milligrams per liter. A random sample of 10 precipitation dates in 2007 results in the following:
0.079, 0.179, 0.078, 0.132, 0.074, 0.225, 0.262, 0.339. 0.111, 0.119
Construct a 98% confidence interval about the sample mean concentration of calcium precipitation.
A- State the hypothesis
B- test statistic??
C- P value ??
D- Reject or fail to reject? Why?

please include lower and upper bound

Solutions

Expert Solution

Calculate sample mean and sample standard deviation for the given data. We get

Sample mean() = 0.1598

Sample size (n)= 10, =0.12

Sample standard deviation(s)= 0.08980

1)

First calculate 98% confidence interval as follows.

Where tc is t critical value for c=98%

With df= n-1 =10-1 = 9

We calculate critical value using t table we get

tc= 2.821

(0.07968 < <0.02399)

Lower bound=0.07968

Upper bound=0.02399

2)

Ho: = 0.12

Ha: 0.12

Calculate test statistics

t= 1.4015

Calculate P- value using TI-83 calculator we get p- value as follows.

P-value= 0.1946

C= 98% =0.98   =1-c = 1-0.98 = 0.02

Hence  = 0.02

Decision Rule:

If p-value then reject Ho

If p-value > then fail to reject Ho

Here (p- value = 0.1946) > (= 0.02)

Hence fail to reject Ho.


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