BUSINESS STATISTICS

Under faculty business and accountancy subject business statistics

Problem Description:

Cardiovascular diseases (CVDs) are the number 1 cause of death globally, taking an estimated 17.9 million lives each year, which accounts for 31% of all deaths worlwide. Heart failure is a common event caused by CVDs and this dataset contains 12 features that can be used to predict mortality by heart failure. Most cardiovascular diseases can be prevented by addressing behavioural risk factors such as tobacco use, unhealthy diet and obesity, physical inactivity and harmful use of alcohol using population-wide strategies. People with cardiovascular disease or who are at high cardiovascular risk (due to the presence of one or more risk factors such as hypertension, diabetes, hyperlipidaemia or already established disease) need early detection and management. Therefore, the report on the heart failure need to be done. You are part of the research team that conduct on this research. Then, your and team are needed to prepare a report on the Cardiovascular diseases (CVDs). You will use descriptive statistics and your knowledge of continuous distributions to complete this task. Data are given in csv format.

Data description:

#age age

#anamea - Decrease of red blood cells or hemoglobin (boolean)

# creatinine_phosphokinase - Level of the CPK enzyme in the blood (mcg/L)

# diabetes 1(yes),0(No)

# ejection_fraction - Percentage of blood leaving the heart at each contraction (percentage)

# high_blood_pressure -1(yes),0(No) # platelets - Platelets in the blood (kiloplatelets/mL)

# serum_creatinine - Level of serum creatinine in the blood (mg/dL)

# serum_sodium - Level of serum sodium in the blood (mEq/L) #sex- 1(Female),0(Male) #smoking -1(yes),0(No)

#time - Follow-up period (days)

Required:

Randomly select 50 data from dataset, then used the data to estimate descriptive statistics for each of these factors Decrease of red blood cells or hemoglobin (boolean), Level of the CPK enzyme in the blood (mcg/L), Percentage of blood leaving the heart at each contraction (percentage), Platelets in the blood (kiloplatelets/mL), and Level of serum sodium in the blood (mEq/L). Compare all these factors. Be sure to comment on the central tendency, variability and shape of these two investments. Based on your findings, discuss on the mean and variability. Assume that the data are normally distributed with a mean and standard deviation (as estimated in (a) rounded to the nearest integer). Answer the following questions:

i. Find the probability that Level of serum sodium in the blood (mEq/L) will exceed 145(mEq/L)

ii. Find the probability that age exceed 70

iii. Find the probability that Percentage of blood leaving the heart at each contraction (percentage) will be between 35% and 42%.

a. Creatine phosphokinase (CPK) is an enzyme in the body. It is found mainly in the heart, brain, and skeletal muscle. Therefore, what factors does effect level of these enzyme. Test whether there have significant different between gender on level of the CPK enzyme in the blood (mcg/L). Use 0.05 level of significant and interpret your answer.

b. Does percentage of blood leaving the heart at each contraction depend on the on level of the CPK enzyme in the blood (mcg/L)? Construct a scatter plot and interpret the results.

c. Test whether platelets in the blood, level of serum creatinine in the blood, level of serum sodium in the blood effect on level of the CPK enzyme in the blood . Use 0.05 level of significant and interpret your answer.

age 1 2 3 4 anaemia 61 50 45 45 60 smoking time 0 0 1 1 1 0 0 0 1 1 1 1 49 72 42 1 0 1 0 1 0 1 0 67 60 79 59 53 55 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 40 44 51 67 70 42 60 80 creatinine_phosphokinase diabetes ejection_fraction high_blood_pressure platelets serum_creatinine serum_sodium sex 1 84 0 40 1 229000.00 0.90 141 0 250 0 25 0 262000.00 1.00 136 0 582 0 35 0 385000.00 1.00 145 0 582 0 80 0 263358.03 1.18 137 0 68 0 20 0 119000.00 2.90 127 0 789 0 20 1 319000.00 1.10 136 0 364 1 20 1 254000.00 1.30 136 1 250 1 15 0 213000.00 1.30 136 0 582 0 50 0 263358.03 1.18 137 1 76 1 25 0 196000.00 2.50 132 1 55 0 50 1 172000.00 1.80 133 1 280 1 25 1 302000.00 1.00 141 0 56 0 50 0 308000.00 0.70 135 0 66 0 40 0 203000.00 1.00 138 0 582 1 35 0 222000.00 1.00 132 0 582 1 30 1 263358.03 1.60 130 0 582 1 40 0 221000.00 0.90 134 0 213 0 38 0 215000.00 1.20 133 0 582 0 40 0 51000.00 2.70 136 0 64 0 30 0 215000.00 3.80 128 0 582 1 38 1 451000.00 0.60 138 1 553 0 20 1 140000.00 4.40 133 1 129 0 30 0 395000.00 1.00 140 1 577 0 25 1 166000.00 1.00 138 1 91 0 20 1 418000.00 1.40 139 0 0 3964 1 62 0 263358.03 6.80 146 1 69 1 50 1 351000.00 1.00 134 0 109 0 35 0 254000.00 1.10 139 0 582 0 35 0 385000.00 1.00 145 0 582 0 80 0 263358.03 1.18 137 0 68 0 20 0 119000.00 2.90 127 1 250 1 15 0 213000.00 1.30 136 1 110 0 25 0 274000.00 1.00 140 0 161 0 25 0 244000.00 1.20 142 0 113 1 25 0 497000.00 1.83 135 0 148 0 40 0 374000.00 0.80 140 0 582 1 35 0 122000.00 0.90 139 0 0 5882 0 35 0 243000.00 1.00 132 1 111 0 20 0 210000.00 1.90 137 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 1 1 1 1 1 DEATH EVENT 110 0 120 0 61 1 63 0 64 1 55 1 59 1 65 1 76 0 77 1 78 0 78 1 231 0 233 0 244 0 244 0 244 0 245 0 250 0 250 0 40 1 41 1 42 1 43 1 43 1 43 1 44 1 60 0 61 1 63 0 64 1 65 1 65 1 66 1 67 1 68 0 71 0 72 1 7 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 57 68 53 60 70 55 45 45 60 42 72 70 65 41 58 85 50 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 41 42 65 90 75 1 1 1 0 0 0 20 40 15 1 0 0 0 1 0 81 8 10 1 1 1 1 60 1 43 44 45 46 47 48 49 60 65 80 0 1 0 1 1 0 160 47 246 315 157 123 81 231 981 5209 0 0 0 1 1 327000.00 204000.00 127000.00 454000.00 263358.03 388000.00 368000.00 253000.00 136000.00 226000.00 65 35 38 25 30 2.70 2.10 1.20 1.10 1.50 9.40 4.00 0.90 1.10 1.00 116 132 137 131 138 133 131 140 137 140 0 1 1 1 0 1 1 1 1 1 10 10 10 10 1 1 1 1 1 1 0 0 75 62 45 42 1 1 0 1 0 0 0 0 1 10 11 87 1 1 0 50 30 0 age 1 2 3 4 anaemia 61 50 45 45 60 smoking time 0 0 1 1 1 0 0 0 1 1 1 1 49 72 42 1 0 1 0 1 0 1 0 67 60 79 59 53 55 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 40 44 51 67 70 42 60 80 creatinine_phosphokinase diabetes ejection_fraction high_blood_pressure platelets serum_creatinine serum_sodium sex 1 84 0 40 1 229000.00 0.90 141 0 250 0 25 0 262000.00 1.00 136 0 582 0 35 0 385000.00 1.00 145 0 582 0 80 0 263358.03 1.18 137 0 68 0 20 0 119000.00 2.90 127 0 789 0 20 1 319000.00 1.10 136 0 364 1 20 1 254000.00 1.30 136 1 250 1 15 0 213000.00 1.30 136 0 582 0 50 0 263358.03 1.18 137 1 76 1 25 0 196000.00 2.50 132 1 55 0 50 1 172000.00 1.80 133 1 280 1 25 1 302000.00 1.00 141 0 56 0 50 0 308000.00 0.70 135 0 66 0 40 0 203000.00 1.00 138 0 582 1 35 0 222000.00 1.00 132 0 582 1 30 1 263358.03 1.60 130 0 582 1 40 0 221000.00 0.90 134 0 213 0 38 0 215000.00 1.20 133 0 582 0 40 0 51000.00 2.70 136 0 64 0 30 0 215000.00 3.80 128 0 582 1 38 1 451000.00 0.60 138 1 553 0 20 1 140000.00 4.40 133 1 129 0 30 0 395000.00 1.00 140 1 577 0 25 1 166000.00 1.00 138 1 91 0 20 1 418000.00 1.40 139 0 0 3964 1 62 0 263358.03 6.80 146 1 69 1 50 1 351000.00 1.00 134 0 109 0 35 0 254000.00 1.10 139 0 582 0 35 0 385000.00 1.00 145 0 582 0 80 0 263358.03 1.18 137 0 68 0 20 0 119000.00 2.90 127 1 250 1 15 0 213000.00 1.30 136 1 110 0 25 0 274000.00 1.00 140 0 161 0 25 0 244000.00 1.20 142 0 113 1 25 0 497000.00 1.83 135 0 148 0 40 0 374000.00 0.80 140 0 582 1 35 0 122000.00 0.90 139 0 0 5882 0 35 0 243000.00 1.00 132 1 111 0 20 0 210000.00 1.90 137 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 1 1 1 1 1 DEATH EVENT 110 0 120 0 61 1 63 0 64 1 55 1 59 1 65 1 76 0 77 1 78 0 78 1 231 0 233 0 244 0 244 0 244 0 245 0 250 0 250 0 40 1 41 1 42 1 43 1 43 1 43 1 44 1 60 0 61 1 63 0 64 1 65 1 65 1 66 1 67 1 68 0 71 0 72 1 7 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 57 68 53 60 70 55 45 45 60 42 72 70 65 41 58 85 50 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 41 42 65 90 75 1 1 1 0 0 0 20 40 15 1 0 0 0 1 0 81 8 10 1 1 1 1 60 1 43 44 45 46 47 48 49 60 65 80 0 1 0 1 1 0 160 47 246 315 157 123 81 231 981 5209 0 0 0 1 1 327000.00 204000.00 127000.00 454000.00 263358.03 388000.00 368000.00 253000.00 136000.00 226000.00 65 35 38 25 30 2.70 2.10 1.20 1.10 1.50 9.40 4.00 0.90 1.10 1.00 116 132 137 131 138 133 131 140 137 140 0 1 1 1 0 1 1 1 1 1 10 10 10 10 1 1 1 1 1 1 0 0 75 62 45 42 1 1 0 1 0 0 0 0 1 10 11 87 1 1 0 50 30 0