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10.3.27 Question Help 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. Complete parts (a) through (c) below. Click the icon to view the data table 0,11 mg/L нер + 0.11 mgr (b) Construct a 98% 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.) Enter your answer in the edit fields and then click Check Answer. part Clear All Check Answer

Answer 1

Given,

The sample mean is,

$\small \bar{x} = 0.15$

The sample standard devaition is,

$\small s = 0.09$

Number of samples

$\small n = 10$

a)

$\small H_0:\mu = 0.11$

$\small H_1:\mu \neq 0.11$

we now that the test statistic is,

$\small t= \frac{\bar{x} - 0.11}{ \frac{s} {\sqrt{n}}}$

t = 1.4055

The corresponding p value is 0.1935

At 0.05 significance level we fail to reject the null hypothesis.

b)

$\small Confidence\; Interval = \bar{x} \pm z * \frac{s} {\sqrt{n}}$

where z score corresponding to 98% Confidence is 2.82

$\small Confidence\; Interval = 0.15 \pm 2.82 * \frac{0.09} {\sqrt{10}}$

$\small Confidence\; Interval =[0.0697 \; , \; 0.2303]$

Therefore,

the lower bound = 0.0697

the upper bound = 0.2303