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The question was too long to fit in one photo, Lotion B's stats are the bottom cut out area. Thank you!! Many dermatologists use a

The question was too long to fit in one photo, Lotion B's stats are the bottom cut out area. Thank you!!

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Many dermatologists use a quantitative description analysis (QDA) to describe the quality of a patient's skin, where they use a standard process to rate the skin from to 10, with higher values indicating healthier skin. A researcher conducted a study to investigate whether two lotions are different in promoting healthy skin for patients who have already seen a dermatologist. The researcher randomly assigned 70 patients from a local hospital to receive one of the two lotions. with 35 receiving Lotion A and receiving Lotion B. At the end of the study, a dermatologist, who was not aware of each patient's assigned lotion, determined the QDA score for each patient. The results of the study are shown in the following dotplots. Lotion A ........... ......... ...... -... 0 1 2 3 4 5 6 8 9 10 QDA Score Lotion B -.... 2 4 5 6 8 9 10 QDA Score (a) Based on the dotplots, write a few sentences comparing the distributions of the scores for the patients who received Lotion A and the patients who received Lotion B. The researcher will conduct a hypothesis test to investigate whether the sample data provide convincing statistical evidence that there is a difference between the two population means. Let JA represent the mean score for all patients similar to those in the study who could have been given Lotion A, and let Up represent the mean score for all patients similar to those in the study who could have been given Lotion B. The hypotheses for the test are as follows. Ho: HA = HB HA HA # HB (b) After examining the two dotplots, the researcher is concerned that the normality condition for the test may not be satisfied. Explain why the researcher should not be concerned. A 95% confidence interval for a difference between the population means (Lotion A minus Lotion B) is 3.1212 + 1.2907. (c) Based on the confidence interval, what conclusion should the researcher make for the hypothesis test? Justify your

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