A Simple Random Sample of 10 Houses in a Particular $7.7$

question 35

Essay

A simple random sample of 10 houses in a particular town was selected and the level of radon gas measured for each house in the sample. The sample mean was $7.7$ parts per million, and the standard deviation $2.98$ parts per million. Experience has shown that radon gas level is approximately normally distributed in similar populations.
a) Construct and interpret a $99 \%$ confidence interval for $\mu$ .
b) The city standards for radon call for a radon level of no more than $6 \mathrm { ppm }$ . Based on your answer to part (a), does it appear that the mean radon level for city houses is greater than 6 ppm? Provide statistical justification for your response.

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Definitions:

Radiant Temperature

The measure of the heat emission or absorption by objects and surfaces through electromagnetic radiation, affecting thermal comfort.

Skin Moisture

The presence of water in the outer layer of the skin, which is crucial for maintaining skin elasticity, preventing dryness, and protecting against irritation and damage.

Oxygen Saturation

A measure of the amount of oxygen-carrying hemoglobin in the blood relative to the amount of hemoglobin not carrying oxygen.

Peripheral Vascular Disease

A circulatory condition in which narrowed blood vessels reduce blood flow to the limbs, leading to symptoms such as pain, numbness, and in severe cases, tissue death.