s3892314 Business Statistics 1 Assignment 2 PDF

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 BUSINESS STATISTICS 1 - ASSIGNMENT 2 -DATASET: 06 - MORTALITY RATE NEONATALBY LE NGOC HUEID : sWord count: 2963.I. Introduction. Decreasing the neonatal mortality rate has become a huge concern in social policy, public health (Treiber 2017). Between 1990 and 2017, the global neonatal death rate dr...

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BUSINESS STATISTICS 1 - ASSIGNMENT 2 DATASET: 06 - MORTALITY RATE NEONATAL BY LE NGOC HUE ID: s3892314 Word count: 2963.

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I. Introduction. Decreasing the neonatal mortality rate has become a huge concern in social policy, public health (Treiber 2017). Between 1990 and 2017, the global neonatal death rate dropped by 51% (United Nations Inter-agency Group for Child Mortality Estimation 2018), however, it still remains high, with more countries are predicted to fail the neonatal mortality target in 2030 (UNICEF n.d), because neonatal death in the highest-risk countries are 50 times more likely to occur than in the lowest mortality country, and it declined more slowly than under-five mortality (UNICEF n.d) Decreasing the neonatal mortality rate plays a crucial part in meeting the United Nations SDG 3 (The Global Goals n.d) because the neonatal death rate is an essential indication of a community's overall physical health (Treiber 2017). Furthermore, high neonatal death rates are frequently indicative of unfulfilled human health needs in hygiene, nutrition, healthcare, suggesting that the country's SDG 3 goal of guaranteeing healthy lives and promoting well-being for all ages remains unreachable (Treiber 2017). According to UNICEF (n.d), neonatal mortality worldwide remains alarmingly high, especially in the poorest countries, implying a strong negative relationship between the neonatal mortality rate and gross national income (GNI) (Neal & Falkingham 2014). GNI is a criterion for classifying economies (Jalal, Khan & Younis 2016), whereas neonatal mortality rate is a helpful indication of a country's level of growth or health (Jalal, Khan & Younis 2016). It is stated that the average neonatal mortality rate in low-income nations is much higher than in highincome countries (UNICEF n.d). It is because residents of these wealthy nations can easily access cutting-edge medical facilities (Jalal, Khan & Younis 2016), improved contextual factors (income, sanitation) (Neal & Falkingham 2014), high coverage of excellent prenatal care as well as timely health interventions (World Health Organization 2020), thus, they naturally have a lower neonatal mortality rate than those in less developed countries (Jalal, Khan & Younis 2016). Conversely, low and middle-income countries frequently account for the great majority of neonatal mortality (World Health Organization 2020) due to a lack of resources to invest in healthcare systems, resulting in a very high rate of impact of poor health, which in turn affects Gross National Income (Jalal, Khan & Younis 2016). II. Descriptive Statistics and Probability. 1. Probability. Conditional probability, as defined by Berenson and Levine (2018), is when the likelihood of one incidence depends on the occurrence of others. Specifically: P(high rate): the probability of high mortality rate neonatal in 2017. P(nI): the probability of The Gross National Income made in three countries categories in 2017. The probability of mortality rate neonatal in each country category, P(high rate ∩ nI), will be divided by the marginal probability, P(nI), to establish if the Mortality rate neonatal is dependent on the GNI or not. Therefore, P(high rate|nI) is the probability of the nations' neonatal mortality rate. If this P(high rate |nI) = P(high rate) equation holds true, the two events are considered independent (Holmes, Illowsky & Dean 2015). Otherwise, the neonatal mortality rate and the GNI are interdependent. Use “DP1000LB” as the abbreviation for “deaths per 1,000 live births”. 2

High mortality rate neonatal (>15 DP1000LB)

Low mortality rate neonatal (

8.60

33.3 0

<

44.20

No outliers

MiddleIncome

1.80

>

-8.10

35.5 0

>

35.24

1 Outlier

countries High-Income countries

0.90

>

0.05

4.70

>

3.65

2 Outliers

Table 2: Table of tests of outliers. Measures of Central Tendency

Low-income countries

Middle-income countries

High-income countries

26.12 DP1000LB

14.06 DP1000LB

2.25 DP1000LB

25 DP1000LB

12,40 DP1000LB

2 DP1000LB

N/A

N/A

Mean

Median

Mode

2.2 DP1000LB

Table 3: Measures of Central Tendency of three countries categories on mortality rate neonatal. Table 3 is calculated after the application of the IQR rules has determined that there are outliers in the dataset since the maximums of both middle-income and high-income countries are larger than their upper bounds. As seen in Table 3, all measures of low-income countries are greater than middle-income countries and high-income countries, demonstrating that the low-income group has witnessed the highest neonatal mortality rate. Furthermore, the high-income countries’ median is the lowest, indicating the high-income countries’ 2017 neonatal mortality rate is pretty lower than that of the other 2 remanding. However, Table 2 is demonstrated a total of 1 outlier in the middle-income group dataset and 2 outliers in high-income ones. When there are outliers in the dataset, Manikandan (2011) believes that the median is preferable to the mean because it can compensate for the distortion caused by extreme values while the mean is stated to be sensitive to extreme values (Manikandan 2011). Furthermore, the data's mode of low and middle-income countries is undetectable. Therefore, the median is the ideal metric for assessing this data due to its ability to counteract the distortion of extreme values. b) Variation. Measures of Variation

Low-income countries

Middle-income countries

High-income countries

12.40 DP1000LB

33.70 DP1000LB

3.80 DP1000LB

Range

4

Interquartile Range (IQR) 8.90 DP1000LB

Sample Variance 19.00 DP1000LB squared

10.83 DP1000LB

0.90 DP1000LB

69.21 DP1000LB squared

1.48 DP1000LB squared

Standard Deviation 4.87 DP1000LB

8.47 DP1000LB 1.28 DP1000LB

Coefficient of Variation

0.19%

0.60%

0.57%

Table 4: Measures of Variation of three countries categories on mortality rate neonatal. Moving to table 4, it can be seen that all the middle-income countries’ measures of variation are the highest compared to those of both low and high-income countries, with the gap between them being fairly substantial. The IQR is the optimum metric in this case since the data contain extreme values (Whaley III 2005). Its unaffected by extreme value makes IQR superior to the standard deviation and the range since both of them are sensitive to outliers (Manikadan 2011). Furthermore, the standard deviation represents the dispersion around the mean, hence, calculating the standard deviation when utilizing the median as a metric of central tendency is impractical (Whaley III 2005). Manikadan (2011) also noted that the middle half of all observations is described by the IQR. This means that the lower a data value's IQR is, the closer to the mean the center half of the data is, thus the less variance the data has (Whaley III 2005). Consequently, data from middle-income countries have a more fluctuated IQR than data from other remaining, implying that middle-income countries’ neonatal mortality rate is more spread out and dispersed. III. Confidence interval (CI). 1. Calculate CI. 0.95 0.05 Confidence Significance 0.025 level level ( 1 ― �) �

5

9.85

Sample standard deviation ()

Population standard deviation (� )

12.51

Population mean (� )

Sample mean ( )

45 Sample size ()

t-critical value (t)

44 Degree freedom (d.f)

of

± 2.0153

Table 5: Summary of Inferential Statistics of the dataset. Since the population standard deviation is unknown, the sample standard deviations are utilized instead of the population standard deviations (Holmes, Illowsky & Dean 2015). Furthermore, Hartmann, Krois & Waske (2018) also noted that instead of using the normal distribution, the Student's t-distribution should be used as a consequence of the lack of population standard deviation. Furthermore, a confidence level of 95% was used to determine the CI of given datasets, leading to the estimated significant level is 0.05. The needed values have been computed and shown in Table 5 sequentially. Following that, the CI is calculated using the equations below: ⇒ ⇒9.55

15.47

In conclusion, it is 95% confident that the population mean of global neonatal mortality rate is between 9.55 DP1000LB and 15.47 DP1000LB. 2. Discussing assumptions. As stated by Siegel (2016), according to the Central Limit Theorem (CLT), as the sample size is larger than 30, it will be approximately normally distributed regardless of the population 6

distribution. Consequently, though the population standard deviation is unknown, no assumptions are required for the computation of the CI because the sample size is 45, which is greater than the standard of 30.

3. Impact on the CI results. Since the global standard deviation of each Mortality rate neonatal ( is given, the normal distribution would be used (Figure 2) (Hartmann, Krois & Waske 2018). Whether is known or unknown, the sample given would stay the same in both cases, therefore the sample mean and the sample size would be unchanged. Using the same 95% of confidence level in the given scenario, the significance level value would be the same, therefore, the t-critical value would larger than the z- critical value since the t-distribution tend to have a fatter tail, accounting for the fact that the area for unlikely value is broader compared to the z-distribution (Hayes 2021), leading to decrease non-rejection region, then the CI would reduce when the is known. However, it is not enough evidence to conclude because it is impossible to confirm the population standard deviation (σ) is smaller than the sample standard deviation (S) since a lot of samples could be chosen randomly due to the random sampling process. Therefore, 3 assumptions are made to examine after concluding: 

Assumption 1: .

In this scenario, all the value is unchanged except the critical values. As stated above, the tcritical values would be larger than the z-critical values, leading to the CI would decrease when the � is known. 

Assumption 2: .

With the t-critical value larger than the z-critical value, combined with the assumption which made the CI result even larger since and have a positive relationship (Figure 1), hence the CI would decrease when � is known. 

Assumption 3:

The t-critical value is larger than the z-critical value, however, with the assumption , it is impossible to conclude in this scenario.

Figure 1: The formula of CI estimate with an unknown � (case 1).

Figure 2: The formula of CI estimate with a known �. 7

After three assumptions are considered, it is concluded that a decrease would be the possible impact on the CI result when the is given. This will reduce the uncertainty, hence the accuracy is more enhanced (Nica 2013). VI. Hypothesis testing. a) Hypothesis testing. The global average neonatal mortality rate given was 18.6 DP1000LB, which is higher than the mean of the dataset (12.51 DP1000LB). However, due to the possibility of error of the random sampling, the 95% CI should be considered. Still, when this mean is applied to the CI, the upper limit of the CI is likewise lower than the hypothetical mean (15.47. Hazra, A 2017, ‘Using the confidence interval confidently’, Journal of thoracic disease, vol.9, no.10, pp. 4125. Holmes, A, Illowsky, B & Dean, S 2015, Introductory Business Statistics, OSCRiceUniversity, viewed 16 August 2021, . Jalal, S, Khan, N-U, & Younis, M-Z 2016, ‘Effect of GNI on Infant Mortality Rate in Low Income, Lower Middle Income, Upper Middle Income and High Income Countries’, Journal of health and human services administration, pp. 159-185. Lumen 2017, Concepts in Statistics, Lumen, viewed 29 April 2021, . Manikandan, S 2011, ‘Measures of Pharmacotherapeutics, vol.2, no.4, pp.315.

dispersion’,

Journal

of

Pharmacology

and

Manikandan, S 2011, ‘Measures of central tendency: Median and mode’, Journal of Pharmacology and Pharmacotherapeutics, vol. 2, no. 3, pp. 214-215. Manikandan, S 2011, ‘Measures of central tendency: The mean’, Journal of Pharmacology and Pharmacotherapeutics, vol.2, no.2, pp. 140. Mc Leod, S 2019, ‘What is central limit theorem in statistics’, Simply psychology, viewed 15 August 2021, . Neal, S, & Falkingham, J 2014, ‘Neonatal death and national income in developing countries: will economic growth reduce deaths in the first month of life?’, International Journal of Population Research, 2014, pp.1-6. Nica, M 2013, Principles of Business Statistics, OpenStax CNX, viewed 20 August 2021, . Siegel, A. 2016, Practical business statistics. Academic Press. 11

Treiber, L-A 2017, ‘Infant mortality rate’, Encyclopedia Britannica, 16 August, viewed at 14 August 2021, . The Global Goals n.d, 3 good health and well-being, The Global Goals, viewed 14 August 2014, . United Nations Inter-agency Group for Child Mortality Estimation 2018, Levels & Trends in Child Mortality: Report 2018, UNICEF, Newyork. UNICEF n.d, Thế giới đang thất bại đối với trẻ sơ sinh, theo UNICEF,UNICEF, viewed 14 August 2021, . World Health Organization 2020, Newborns: improving survival and well-being, World Health Organization, viewed 15 August 2021, . Whaley III, D. L 2005, ‘The interquartile range: Theory and estimation, Doctoral dissertation, East Tennessee State University, viewed 16 August 2021, .

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