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# Calcium in Chautauqua's Rain: 1990 vs. 2010 Analysis

**Chapter 6, Problem 23**

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**QUESTION:**

Calcium in Rainwater 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 Chautauqua, New York, was 0.11 milligram per liter (mg/L). A random sample of 10 precipitation dates in 2010 results in the following data:

0.065 |
0.087 |
0.070 |
0.262 |
0.126 |

0.183 |
0.120 |
0.234 |
0.313 |
0.108 |

Source: National Atmospheric Deposition Program |

(a) Because the sample size is small, we must verify that calcium concentrations are normally distributed and the sample does not have any outliers. The normal probability plot and boxplot are shown. Are the conditions for conducting the hypothesis test satisfied?

(b) Does the sample evidence suggest that calcium concentrations have changed since 1990? Use the \(\alpha=0.05\) level of significance.

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##### Calcium in Chautauqua's Rain: 1990 vs. 2010 Analysis

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Explore the calcium concentration in Chautauqua's rainwater from 2010, comparing it to 1990 levels. Using statistical tests, examine normal distribution and determine significant changes. The results provide insights into environmental shifts over two decades.

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### Questions & Answers

**QUESTION:**

Calcium in Rainwater 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 Chautauqua, New York, was 0.11 milligram per liter (mg/L). A random sample of 10 precipitation dates in 2010 results in the following data:

0.065 |
0.087 |
0.070 |
0.262 |
0.126 |

0.183 |
0.120 |
0.234 |
0.313 |
0.108 |

Source: National Atmospheric Deposition Program |

(a) Because the sample size is small, we must verify that calcium concentrations are normally distributed and the sample does not have any outliers. The normal probability plot and boxplot are shown. Are the conditions for conducting the hypothesis test satisfied?

(b) Does the sample evidence suggest that calcium concentrations have changed since 1990? Use the \(\alpha=0.05\) level of significance.

**ANSWER:**

Step 1 of 3

(a) Yes, all the data lie within the confidence bands of the normal probability plot, and the boxplot does not show any outliers.

(b) Hypothesis

\(\begin{array}{l}

H_{0}: \mu=0.11 \\

H_{1}: \mu \neq 0.11

\end{array}\)