Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concern in a number of different locales. The article "Airborned Hexavalent Chromium in Southwestern Ontario" (J. of Air and Waste Mgmnt. Assoc., 1997: 905-910) gave the accompanying data on both indoor and outdoor concentration (nanograms/m^3) for a sample of houses selected from a certain region.
House
--------------------------------------------------
1 2 3 4 5 6 7 8 9
---------------------------------------------------
Indoor .07 .08 .09 .12 .12 .12 .13 .14 .15
Outdoor .29 .68 .47 .54 .97 .35 .49 .84 .86
---------------------------------------------------
House
--------------------------------------------------
10 11 12 13 14 15 16 17
-----------------------------------------------
Indoor .15 .17 .17 .18 .18 .18 .18 .19
Outdoor .28 .32 .32 1.55 .66 .29 .21 1.02
-----------------------------------------------
House
-----------------------------------------------
18 19 20 21 22 23 24 25
------------------------------------------------
Indoor .20 .22 .22 .23 .23 .25 .26 .28
Outdoor 1.59 .90 .52 .12 .54 .88 .49 1.24
------------------------------------------------
House
-----------------------------------------------
26 27 28 29 30 31 32 33
------------------------------------------------
Indoor .28 .29 .34 .39 .40 .45 .54 .62
Outdoor .48 .27 .37 1.26 .70 .76 .99 .36
------------------------------------------------
a. find out a confidence interval for the population mean difference between indoor and outdoor concentrations using a confidence level of 95%, and interpret the resulting interval.
b. If a 34th house were to be randomly selected from the population, between what values would you predict the difference in concentrations to lie?
c. Construct the 95% confidence intervals for the indoor and for the outdoor true concentration. Do these CIs overlap, and what does that imply about the hypothesis test in part(a)? prepare a paragraph justifying your answer.