Question

calcium is essential to tree growth. in 1990, the concentration of calcium in precipitation in chautauqua, new york, was 0.11 milligram per liter (\\( \frac { m g } { l } \\)). a random sample of 8 precipitation dates in 2018 results in the following data.
0.070 0.108 0.120 0.262 0.065 0.234 0.126 0.087
a normal probability plot suggests the data could come from a population that is normally distributed. a boxplot does not show any outliers. does the sample evidence suggest that calcium concentrations have changed since 1990? use the \\( \alpha = 0.05 \\) level of significance.
what are the null and alternative hypotheses?
\\( h _ { 0 } \\) \\( \mu = 0.11 \\)
\\( h _ { 1 } \\) \\( \mu \
eq 0.11 \\)
(type integers or decimals. do not round.)
find the test statistic.
\\( t _ { 0 } = 0.92 \\) (round to two decimal places as needed.)
find the p - value.
\\( p \text { -value } = \square \\) (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 8\). So \(df=8-1 = 7\)

Step2: Use the t - distribution to find the P - value

Since the test is two - tailed (because \(H_1:\mu
eq0.11\)) and \(t_0 = 0.92\).
We use the t - distribution table or a calculator. Using a calculator (for example, in R: \(2*(1 - pt(0.92,7))\)), where \(pt\) is the cumulative distribution function of the t - distribution.
\(P - value=2(1 - 0.807)=20.193 = 0.386\)

Answer:

\(0.386\)