Skylar Pelletier
Enes Ozel
STAT 201 Sec 009
December 1, 2023
Executive Report for Knoxville Health Solutions:
Diabetes Rates, BMI, and Body Fat Percentages Amongst Individuals
Executive Summary
This report explores the relationships between the rates of diabetes, body fat
distribution, and BMI within our sample population of 461 individuals. The bar chart highlights
the possible health concerns regarding the number of individuals with diabetes. It is revealed
that 34.06% of the individuals sampled do have diabetes, while the remaining 65.94% of those
samples reported not having diabetes. Then, a 95% confidence interval for diabetes prevalence
was then run, suggesting the true proportion of individuals with diabetes is between 29.88% to
38.5%, which challenges the assumption that 50% of individuals have diabetes. A hypothesis
test confirms there is a statistically significant divergence from our company’s estimate,
indicative that the prevalence of diabetes is lower than to be expected.
When looking at body fat distribution, we see unimodal histogram with a mean of 32.88
pounds, with a range of 47.7 pounds, and a standard deviation of 6.79 pounds. We then ran
another confidence interval, this time at a 99% confidence, which resulted in the true mean
being within 27.86 and 30.40 pounds. The scatterplot regression analysis explores the
connection between body fat and BMI, which revealed a positive correlation. From the model,
we can suggest that 43.5% of the variation in body fat can be attributed to BMI, and with our p
value of <0.0001, indicating there is statistical significance in this correlation.
In conclusion, this report recognizes the vital need for future endeavors to enhance our
understanding of diabetes and its correlation to both body fat and BMI. Moving forward, our
research recommends intend to explore the impact of genetic factors on diabetes, the
correlations between certain lifestyle habits and BMI/body fat. These measures hope to deliver
a more thorough understanding as we expand our research in the future.
One Sample Z
, The bar chart and frequency table above show the distribution of individuals from our
sample that have diabetes versus those that did not report having diabetes. Of the 461
individuals, 304 reported they do not have diabetes, while almost exactly half of that number
reported having diabetes, standing at 157 people. The frequencies were reported at 65.94% and
34.06% respectively.
The second representation above illustrates a confidence interval concerning individuals
with and without diabetes. When dealing with categorical variables, it is crucial to verify three
conditions: the sample must be chosen at random, it must be less than 10% of the population,
and the success/failure condition must be met as well. We defined the “success” as not having
diabetes. For the condition to be met, both sample size*sample proportion and sample size*(1-
sample proportion) must be greater than 10. In our case, the success is 304 and the failure is
157, which passes the condition. We can also assume the rest of the conditions are met as well.
A 95% confidence interval was run to determine the true proportion of individuals with
diabetes. This interval affirms that we are 95% confident that the actual percentage of people
with diabetes lies within the range of 29.88% to 34.05%. Despite this interval, our company
speculates that the true proportion is 0.5. As researchers, it is our responsibility to test this
hypothesis for significance and whether there is enough evidence to support our claim.
We will establish our null hypothesisH 0() as the proportion p( 0) is equal to 0.5, and our
alternative hypothesisH(a ) as the proportion p( a) is not equal to 0.5. The results show that our
data has a p-value of essentially 0, suggesting we can reject the null hypothesis due to sufficient
evidence supporting the alternative hypothesis. This means that our company’s assumption that
the true proportion of individuals with diabetes is equal to 0.5 was incorrect. Although this is
not such great news for our company, it does suggest that the prevalence of diabetes is much
less than initially expected.
Enes Ozel
STAT 201 Sec 009
December 1, 2023
Executive Report for Knoxville Health Solutions:
Diabetes Rates, BMI, and Body Fat Percentages Amongst Individuals
Executive Summary
This report explores the relationships between the rates of diabetes, body fat
distribution, and BMI within our sample population of 461 individuals. The bar chart highlights
the possible health concerns regarding the number of individuals with diabetes. It is revealed
that 34.06% of the individuals sampled do have diabetes, while the remaining 65.94% of those
samples reported not having diabetes. Then, a 95% confidence interval for diabetes prevalence
was then run, suggesting the true proportion of individuals with diabetes is between 29.88% to
38.5%, which challenges the assumption that 50% of individuals have diabetes. A hypothesis
test confirms there is a statistically significant divergence from our company’s estimate,
indicative that the prevalence of diabetes is lower than to be expected.
When looking at body fat distribution, we see unimodal histogram with a mean of 32.88
pounds, with a range of 47.7 pounds, and a standard deviation of 6.79 pounds. We then ran
another confidence interval, this time at a 99% confidence, which resulted in the true mean
being within 27.86 and 30.40 pounds. The scatterplot regression analysis explores the
connection between body fat and BMI, which revealed a positive correlation. From the model,
we can suggest that 43.5% of the variation in body fat can be attributed to BMI, and with our p
value of <0.0001, indicating there is statistical significance in this correlation.
In conclusion, this report recognizes the vital need for future endeavors to enhance our
understanding of diabetes and its correlation to both body fat and BMI. Moving forward, our
research recommends intend to explore the impact of genetic factors on diabetes, the
correlations between certain lifestyle habits and BMI/body fat. These measures hope to deliver
a more thorough understanding as we expand our research in the future.
One Sample Z
, The bar chart and frequency table above show the distribution of individuals from our
sample that have diabetes versus those that did not report having diabetes. Of the 461
individuals, 304 reported they do not have diabetes, while almost exactly half of that number
reported having diabetes, standing at 157 people. The frequencies were reported at 65.94% and
34.06% respectively.
The second representation above illustrates a confidence interval concerning individuals
with and without diabetes. When dealing with categorical variables, it is crucial to verify three
conditions: the sample must be chosen at random, it must be less than 10% of the population,
and the success/failure condition must be met as well. We defined the “success” as not having
diabetes. For the condition to be met, both sample size*sample proportion and sample size*(1-
sample proportion) must be greater than 10. In our case, the success is 304 and the failure is
157, which passes the condition. We can also assume the rest of the conditions are met as well.
A 95% confidence interval was run to determine the true proportion of individuals with
diabetes. This interval affirms that we are 95% confident that the actual percentage of people
with diabetes lies within the range of 29.88% to 34.05%. Despite this interval, our company
speculates that the true proportion is 0.5. As researchers, it is our responsibility to test this
hypothesis for significance and whether there is enough evidence to support our claim.
We will establish our null hypothesisH 0() as the proportion p( 0) is equal to 0.5, and our
alternative hypothesisH(a ) as the proportion p( a) is not equal to 0.5. The results show that our
data has a p-value of essentially 0, suggesting we can reject the null hypothesis due to sufficient
evidence supporting the alternative hypothesis. This means that our company’s assumption that
the true proportion of individuals with diabetes is equal to 0.5 was incorrect. Although this is
not such great news for our company, it does suggest that the prevalence of diabetes is much
less than initially expected.
