Radon is a colorless gas 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 12 randomly selected detectors in a chamber where they were exposed to 105 pico curies per liter of radon over 3 days. Here are the readings given by the detectors:

91.9, 97.8, 111.4, 122.3, 105.4, 95.0, 103.8, 99.6, 96.6, 119.3, 104.8, 101.7

Assume that you know the standard deviation of readings for detectors of this type is [tex]\sigma = 9[/tex].

Is there significant evidence at the 10% level that the mean reading differs from the true value of 105?

Therefore , the solution to the given problem of hypothesis comes out to be that there is not sufficient evidence at 10% level to support the claim.

Describe hypothesis.

A hypothesis is a statement that makes sense in light of the available information on confidence interval but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis).

Here,

Given:

90% confidence interval: (99.61,110.03)

Determine the hypotheses:

Null hypothesis [tex]H_{0}[/tex] : u=105

Alternate hypothesis [tex]H_{A}[/tex] : u≠ 105

A significance test at the 10% significance level has a 90% confidence interval.

The confidence range contains 105, thus the claim cannot be supported by the evidence at the 10% level.

As a result, it turns out that there isn't enough evidence to back the claim at a 10% level, which is the answer to the problem at hand.

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