Avobenzone is one of the active ingredients in several commercially available sunscreens. It can be absorbed into the bloodstream when sunscreen is applied to the skin. The Food and Drug Administration has expressed concern about the safety of absorbing too much avobenzone. Researchers recruited 24 healthy volunteers to investigate avobenzone absorption for four different commercially available sunscreens: two sprays, a lotion, and a cream. Do the types of sunscreens (spray, lotion, and cream) differ in terms of how much avobenzone is absorbed into the blood? Subjects were randomly assigned to one of the four sunscreens, with six subjects for each. Subjects had 2 milligrams of sunscreen per 1 cm? applied to 75% of their body surface area (area outside of normal swimwear) four times per day for four days. The amount of avobenzone absorbed into the bloodstream (in nanograms per milliliter ap-plied, ng/mL) after 150 hours was then measured for each subject. For the purpose of analyzing the data us ing ANOVA, the logarithms of the measurements were used. Thus, for example, a value of 0 corresponds to an absorption of 1 ng/ mL and negative values correspond to absorptions less than 1 ng/ mL. Larger values of the logarithms correspond to larger levels of absorption. Figure 27.13 shows JMP ANOVA output for these data. Show the work on how the values are acquired. a. Do these data satisfy the conditions for ANOVA? b. State Ho and H. for the ANOVA F test and explain in words what ANOVA tests in this setting. c. Report your overall conclusions about whether the types of sunscreen differ in the mean amount of avobenzone absorbed into the bloodstream after 150 hours.
Avobenzone is one of the active ingredients in several commercially available sunscreens. It can be absorbed into the bloodstream when sunscreen is applied to the skin. The Food and Drug Administration has expressed concern about the safety of absorbing too much avobenzone. Researchers recruited 24 healthy volunteers to investigate avobenzone absorption for four different commercially available sunscreens: two sprays, a lotion, and a cream. Do the types of sunscreens (spray, lotion, and cream) differ in terms of how much avobenzone is absorbed into the blood? Subjects were randomly assigned to one of the four sunscreens, with six subjects for each. Subjects had 2 milligrams of sunscreen per 1 cm? applied to 75% of their body surface area (area outside of normal swimwear) four times per day for four days. The amount of avobenzone absorbed into the bloodstream (in nanograms per milliliter ap-plied, ng/mL) after 150 hours was then measured for each subject. For the purpose of analyzing the data us ing ANOVA, the logarithms of the measurements were used. Thus, for example, a value of 0 corresponds to an absorption of 1 ng/ mL and negative values correspond to absorptions less than 1 ng/ mL. Larger values of the logarithms correspond to larger levels of absorption.
Figure 27.13 shows JMP ANOVA output for these data. Show the work on how the values are acquired.
a. Do these data satisfy the conditions for ANOVA?
b. State Ho and H. for the ANOVA F test and explain in words what ANOVA tests in this setting.
c. Report your overall conclusions about whether the types of sunscreen differ in the mean amount of avobenzone absorbed into the bloodstream after 150 hours.
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