Descriptive Statistics for Medical Malpractice Claims

Running head: DESCRIPTIVE STATISTICS
Descriptive Statistics
Name of the Student:
Name of the University:
Author’s Note:

1DESCRIPTIVE STATISTICS
Table of Contents
Introduction:...............................................................................................................................3
1. Descriptive Statistics:.............................................................................................................3
2. Estimation:.........................................................................................................................3
2.a)......................................................................................................................................3
2. b)....................................................................................................................................4
Answer 3................................................................................................................................4
3.a)......................................................................................................................................4
3. b)....................................................................................................................................4
3.c)......................................................................................................................................5
3.d).....................................................................................................................................5
3. e).....................................................................................................................................6
Answer 4................................................................................................................................6
4. a).....................................................................................................................................6
4.b).....................................................................................................................................7
References:.................................................................................................................................9
Appendix:.................................................................................................................................10

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Table of Tables
Table 1......................................................................................................................................12
Table 2......................................................................................................................................12
Table 3......................................................................................................................................12
Table 4......................................................................................................................................13
Table 5......................................................................................................................................14
Table 6......................................................................................................................................15
Table 7.1...................................................................................................................................17
Table 7.2...................................................................................................18
Table 8......................................................................................................................................20
Table 9......................................................................................................................................22
Table 10.1.................................................................................................................................23
Table 10.2................................................................................................24
Table of Figures
Figure 1....................................................................................................................................13
Figure 2....................................................................................................................................14
Figure 3....................................................................................................................................15
Figure 4....................................................................................................................................16
Figure 5....................................................................................................................................19
Figure 6....................................................................................................................................21
Figure 7....................................................................................................................................24
Figure 8....................................................................................................................................26

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To: You
From: Edmond Kendrick
Subject: Analysis of Claims
As per earlier discussion, I have cleaned and simplified the undertaken dataset to eight
variables for your convenience. The cleaned dataset contains information about 200 randomly
selected claims promised this year.
Introduction:
The medical malpractice of United States is a severe problem these days as reported
in US News and World report. It consumes a significant segment of total expenditure of the
USA households. The physicians who are mal-practicing are claiming unjustified amount
from the patients. The struggling people not only contribute a high cost of healthcare, but also
contribute a high premium for medical insurance due to malpractices.
The preliminarily collected data is under inspection to justify the true scenario of
medical situations (Pearson 2013). In the followings, descriptive and inferential analysis is
carried out in the surveyed data.
1. Descriptive Statistics:
The descriptive statistics of “Amount” of the Claim payment indicates that-
 The average amount of the claim payment is 73457.49 Australian dollar.
 The claim payment has highest frequency for the amount 5400 Australian dollar.
 The lowest amount of claim payment is 1547 Australian dollar.
 The highest amount of claim payment is 228724.8 Australian dollar.
 The range of amount of claim payment is 227177.8 Australian dollar.
 The 95% of the observations lies in the interval (73457.49±4486.92) Australian dollar
= (77944.41, 68970.58) Australian dollar (Weiss and Weiss 2012).

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2. Estimation:
Answer 2.a)
It is observed that-
The calculated average age of the claimants is 44.49 years. In the dataset of 200 samples, the
interval lower limit of 95% confidence interval is calculated as (44.49-2.4669) = 42.02 years.
The interval upper limit of 95% confidence interval is calculated as (44.49 + 2.4669) = 46.96
years. Therefore, it is estimated that average age of 200 samples lie in the interval of 42.02
years and 46.96 years with 95% probability. Therefore, 95% of the ages of total claimants are
estimated to lie in the interval of 42.02 years and 46.96 years.
Answer 2. b)
Out of 200 samples, the number of claimants with the insurance level “No Insurance” is 18.
The calculated proportion is 0.09. The upper limit of the proportion of claimants with “No
Insurance” is given by 12.97%. The lower limit of the proportion of claimants with “No
Insurance” is 5.03%. Hence, it is 95% evident that the proportion of claimants with “No
insurance” lies in the range of 5.03% and 12.97%. Therefore, it is 95% evident that the
estimated proportion of claimants who do not have insurance would lie in the interval of
5.03% and 12.97% (Montgomery, Runger and Hubele 2009).
Answer 3.
Answer 3.a)
We assume the null hypothesis (H0) as the average paid claim amount is greater than or equal
to $77,500 Australian dollar. The alternative hypothesis (H1), the average amount of paid
claim is less than $77,500 Australian dollar.
The calculated sample average is $73457.49 with the sample size 200. The level of
significance is 0.05. Therefore, the null hypothesis is rejected with 95% probability. The
alternative hypothesis is accepted. Hence, it could be concluded that average amount of paid
claims has dropped below $77,500. It could be concluded that there is no evidence that the
average paid claim amount is greater than or equal to the hypothesised amount.
Answer 3. b)
A study had reported that 3 out of 4 claims are either “MILD” or “MEDIUM” severity
conditions. The calculated count of success is 154 and sample size is 200. Sample proportion
is 0.77. The sample proportion is greater than 75% (3 out of 4). Here, the null hypothesis is

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failed to be rejected with 95% probability. Hence, it could be concluded that the proportion of
severity conditions of “MILD” and “MEDIUM” is at least 75% with respect to all the
severity conditions. Therefore, it could be interpreted that according to all the severity
conditions, the proportion of insurance claimants of “MILD” and “MEDIUM” severity is
greater than or equals to 75%. The inference has enough evidence about severity
measurement.
Answer 3.c)
Now, we would like to find the significant difference between the proportions of “MILD”
and “MEDIUM” insurance claims in accordance to the gender of the patients. The difference
in proportion of “MILD” or “MEDIUM” claims by female patients compared to the male
patients is calculated.
Out of 154 samples whose severity conditions are either “MILD” or “MEDIUM”, 60 are
males and 94 are females. The sample proportions of males and females are 38.96% (Π1) and
61.04% (Π2). The null hypothesis of equality of proportions of frequencies of males and
females is rejected at 5% level of significance. Hence, the difference of proportions is
prominent with 95% probability (Olive 2014). There is a difference in proportion of “MILD”
and “MEDIUM” insurance claims by genders of patients. Therefore, gender has an effect on
the proportions of severity conditions alike “MILD” and “MEDIUM” severity according to
the insurance claimant.
Answer 3.d)
As per the standard of industry, it could be hypothecated that the insurance payment amounts
are related to the private attorney of the claimants. The average claim amount for the private
attorney is greater than the average claim specifically at no involvement of private attorney.
The average of payment amount of private attorney is $80501.07 for 137 samples (Abbott
2017). The average of payment amount of non-private attorney is $58140.51 for 63 samples.
Null hypothesis assumed that the average payment amount of private attorney and the
average payment amount associated to the non-private attorney are equal. The alternative
hypothesis conversely states that the difference of average payment amount of private
attorney and average payment amount related to non-private attorney is unequal to 0. The null
hypothesis of equality of payment amounts is rejected at 5% level of significance (Abbott 2017). It is