The manufacturer conducted a study to investigate whether a new dental treat is different in minimizing the accumulation of plaque on the teeth of cats than the existing dental treat. The manufacturer randomly assigned 70 cats from a cat sanctuary to receive one of the two dental treats, with 35 receiving the new dental treat and 35 receiving the existing dental treat. At the end of the study, an evaluator, who was not aware of each cat's assigned dental treat, determined the FLT rating for each cat. The two boxplots shown display the results of the study. 32 47 52 59 64 70 83 New Dental Treat 32 40 59 72 95 Existing Dental Treat 30 40 50 60 70 80 90 100 FLT Rating (c) Based on the boxplots, write a few sentences comparing the distributions of the FLT ratings for the cats who received the new dental treat and the cats who received the existing dental treat. The manufacturer will conduct a hypothesis test to investigate whether the sample data provide convincing statistical evidence that the mean FLT rating is different for cats receiving the new dental treat rather than the existing dental treat. (d) Name the appropriate hypothesis test and state, in words, the hypotheses. Assume the conditions for inference have been met. A 96 percent confidence interval for the difference in the mean FLT (new dental treat minus existing) was calculated to be -1.286 ± 8.984. (e) Based only on this confidence interval, is the difference in the mean FLT ratings statistically significant? Justify your answer.
The manufacturer conducted a study to investigate whether a new dental treat is different in minimizing the accumulation of plaque on the teeth of cats than the existing dental treat. The manufacturer randomly assigned 70 cats from a cat sanctuary to receive one of the two dental treats, with 35 receiving the new dental treat and 35 receiving the existing dental treat. At the end of the study, an evaluator, who was not aware of each cat's assigned dental treat, determined the FLT rating for each cat. The two boxplots shown display the results of the study. 32 47 52 59 64 70 83 New Dental Treat 32 40 59 72 95 Existing Dental Treat 30 40 50 60 70 80 90 100 FLT Rating (c) Based on the boxplots, write a few sentences comparing the distributions of the FLT ratings for the cats who received the new dental treat and the cats who received the existing dental treat. The manufacturer will conduct a hypothesis test to investigate whether the sample data provide convincing statistical evidence that the mean FLT rating is different for cats receiving the new dental treat rather than the existing dental treat. (d) Name the appropriate hypothesis test and state, in words, the hypotheses. Assume the conditions for inference have been met. A 96 percent confidence interval for the difference in the mean FLT (new dental treat minus existing) was calculated to be -1.286 ± 8.984. (e) Based only on this confidence interval, is the difference in the mean FLT ratings statistically significant? Justify your answer.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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Transcribed Image Text:The manufacturer conducted a study to investigate whether a new dental treat is different in minimizing
the accumulation of plaque on the teeth of cats than the existing dental treat. The manufacturer randomly
assigned 70 cats from a cat sanctuary to receive one of the two dental treats, with 35 receiving the new
dental treat and 35 receiving the existing dental treat. At the end of the study, an evaluator, who was not
aware of each cat's assigned dental treat, determined the FLT rating for each cat.
The two boxplots shown display the results of the study.
32
47 52
59 64
70
83
New Dental Treat
32
40
59
72
95
Existing Dental Treat
30
40
50
60
70
80
90
100
FLT Rating
(c) Based on the boxplots, write a few sentences comparing the distributions of the FLT ratings for
the cats who received the new dental treat and the cats who received the existing dental treat.
The manufacturer will conduct a hypothesis test to investigate whether the sample data provide
convincing statistical evidence that the mean FLT rating is different for cats receiving the new dental treat
rather than the existing dental treat.
(d) Name the appropriate hypothesis test and state, in words, the hypotheses.
Assume the conditions for inference have been met. A 96 percent confidence interval for the difference in
the mean FLT (new dental treat minus existing) was calculated to be -1.286 + 8.984.
(e) Based only on this confidence interval, is the difference in the mean FLT ratings statistically
significant? Justify your answer.
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