Q.8 - The Practice of Statistics for AP

Question

Radon detectors Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed a random sample of $11$ detectors in a chamber where they were exposed to $105$ picocuries per liter of radon over $3$ days. A graph of the radon readings from the $11$ detectors shows no strong skewness or outliers. The Minitab output below shows the results of a one-sample t interval. Is there significant evidence at the $10\%$ level that the mean reading $\mu$ differs from the true value $105$? Give appropriate evidence to support your answer.

Step-by-Step Solution

Answer

The confidence interval contains $105$, there is not sufficient evidence at the $10\%$ level to support the claim.

Step 1: Given Information

$90\%$ confidence interval: $(99.61,110.03)$.

Step 2: Explanation

Determine the hypotheses:

$H_0:\mu =105$

$H_a:\mu \ne 105$

A $90\%$ confidence interval corresponds with a significance test at the $10\%$ significance level.