It has been hypothesized that allergies result from a lack of early childhood exposure to antigens. If this hypothesis were true, then we would expect allergies to be more common in very hygienic households with low levels of bacteria and other infectious agents. To test this theory, researchers at the University of Colorado sampled the houses of 61 children 9-24 months old and recorded two variables: (1) whether the child tested positive for allergies and (2) the concentration of bacterial endotoxin in the house dust (endotoxin units per ml, EU/ml)1. The following are the endotoxin levels at the homes of the 51 children tested negative for allergies. 708.23 911.60 976.81 1316.63 262.74 9772.08 370.76 229.16 2570.51 891.19 3163.20 1777.65 1288.57 436.23 2631.63 1173.52 911.67 7942.42 740.32 356.92 1175.48 1480.55 2754.61 575.62 573.89 468.26 1000.71 364.22 1025.26 1022.04 645.41 363.57 977.47 1022.75 1860.63 371.13 174.73 399.68 1479.77 2882.96 601.99 1697.32 2291.00 646.49 1176.27 1995.43 955.54 1480.05 456.71 1174.70 5494.22 (a) Make a boxplot for the endotoxin levels at the homes of the 51 children without allergy. Comment on whether it is appropriate to construct a t-confidence interval for the mean endotoxin level at the homes of children without allergy. (b) Make a boxplot of the log of the endotoxin levels at the homes of the 51 children without allergy.Comment on whether it is more appropriate to construct a t confidence interval for the mean of the log endotoxin level at the homes of children without allergy. (c) Construct a 95% t-confidence interval for the mean of the log endotoxin level at the homes of children without allergy.
It has been hypothesized that allergies result from a lack of early childhood exposure to antigens. If this hypothesis were true, then we would expect allergies to be more common in very hygienic households with low levels of bacteria and other infectious agents. To test this theory, researchers at the University of Colorado sampled the houses of 61 children 9-24 months old and recorded two variables: (1) whether the child tested positive for allergies and (2) the concentration of bacterial endotoxin in the house dust (endotoxin units per ml, EU/ml)1. The following are the endotoxin levels at the homes of the 51 children tested negative for allergies.
708.23 911.60 976.81 1316.63 262.74 9772.08 370.76 229.16 2570.51
891.19 3163.20 1777.65 1288.57 436.23 2631.63 1173.52 911.67 7942.42 740.32 356.92 1175.48 1480.55 2754.61 575.62 573.89 468.26 1000.71 364.22 1025.26 1022.04 645.41 363.57 977.47 1022.75 1860.63 371.13 174.73 399.68 1479.77 2882.96 601.99 1697.32 2291.00 646.49 1176.27 1995.43 955.54 1480.05 456.71 1174.70 5494.22
(a) Make a boxplot for the endotoxin levels at the homes of the 51 children without allergy. Comment on whether it is appropriate to construct a t-confidence interval for the mean endotoxin level at the homes of children without allergy.
(b) Make a boxplot of the log of the endotoxin levels at the homes of the 51 children without allergy.Comment on whether it is more appropriate to construct a t confidence interval for the mean of the log endotoxin level at the homes of children without allergy.
(c) Construct a 95% t-confidence interval for the mean of the log endotoxin level at the homes of children without allergy.
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