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. Required:
a. Plot a histogram of bacterial endotoxin levels.
b. Test whether the observed difference in endotoxin levels between the "sensitive" and normal"

[a]. check attachment.

[b]. It can not be said that the difference is ascribed to chance as P-value = 0.001 which is less than <<0.05. That is  P-value = 0.001 <<0.05.

Step-by-step explanation:

Without mincing words let's dive straight into the solution to the question above.

[a]. The drawing showing the histogram of bacterial endotoxin levels is given in the attached picture.

KINDLY NOTE: The data is right-skewed.

[b].  ALLERGIC             MEAN        SE MEAN         STDEV           N

      FALSE                     1510             251                  1789            251

        TRUE                    530              109                 343               10

False - true = difference in a.

Hence, 80 = estimated difference.

For the difference, 95% CI = (434, 1527).

DF = 58, P-value = 0.001, and the T value = 3.59.

Therefore, It can not be said that the difference is ascribed to chance as P-value = 0.001 which is less than <<0.05. That is  P-value = 0.001 <<0.05.