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 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

Answer 1

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.