Question

1. Radon is a colorless gas that is naturally related by rocks and soil and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is a small concern that it may be health hazard. Radom detectors are sold to home owners worried about this risk, but the detectors may be inaccurate. University researches placed 12 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

a), Give the approximate distribution of the mean reading of the sample of detectors.

b), Use the date to find a 90% confidence interval for the mean reading μ for this type of detector.

c), Based on the confidence interval in part b, would you use the brand tested or find another brand?

d) Based on a 95% confidence, would you use the brand tested or find another brand.

Answer 1

(a)

From the given data, the following statistics are calculated:

n = 12

= 1249.6/12 = 104.1333

s = 9.3974

The approximate distribution of the mean is t distribution with mean = 104.1333 and Standard Deviation = 9.3974

(b)

SE = s/

= 9.3974/

= 2.7128

= 0.10

ndf = n - 1 = 12 - 1= 11

From Table, critical values of t = 1.7959

Confidence Interval:

104.1333 (1.7959 X 2.7128)

= 104.1333 4.8719

= (99.2614 , 109.0052)

So,

Confidence Interval:

99.2614 < < 109.0052

(c)

Since 105 is included in the Confidence Interval, based on the Confidence Interval in Part (b), we would use the brand tested.

(d)

SE = s/

= 9.3974/

= 2.7128

= 0.05

ndf = n - 1 = 12 - 1= 11

From Table, critical values of t = 2.2010

Confidence Interval:

104.1333 (2.2010 X 2.7128)

= 104.1333 5.9709

= (98.1624 , 110.1042)

So,

Confidence Interval:

98.1614 < < 110.1042

(c)

Since 105 is included in the Confidence Interval, based on the Confidence Interval in Part (b), we would use the brand testd.