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MPH5041, 2013

Biostatistics for Clinical and Public Health Research

Test 2, Due April 14, 2013 by 11:59pm

Modules Covered: This Test covers Modules 1-3. All questions must be answered using

statistical knowledge in Modules 1-3 only. Required data analysis for Question 1 (SPSS or any

other statistical package can be used).

Assignment General Instructions:

This test is worth 5% of total marks for this subject. It will be marked out of 50

marks.

Please explain the results in plain/simple English (if applies).

Word Limit: Maximum 1200 Words.

Please download the “Test 2” and answer the questions within the WORD LIMIT

stated above and then upload the PDF file of the completed test by April 14,

11:59pm.

You must have a COVER PAGE, PRINT YOUR NAME, no sign required. See the

Section “Assignment and Test” on Moodle for cover page.

Instructions for Submission:

Please don’t add the data description or original tables/graphs given in the Questions to

your “SOLUTION”.

Upload the completed TEST 2 onto Moodle under the “Test 2 Drop Box” section.

Extension: Students seeking an extension should contact Baki Billah before the due date. Please

note that an extension will not be granted without valid grounds (e.g., illness with medical

certificate).

Important Note:

If you submit more than one file as an attachment, only the first file will be assessed and

rest of the files will be ignored, sorry!

Please use solution for Test 1 as a guideline for Question 1.

PLEASE DON’T discuss any of these questions on Discussion Forum.

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Data Description: Consider a study that was conducted to investigate the risk factors for

mortality in cardiac surgery patients. Data was collected on Cardiac Surgery patients in public

hospitals in St Martine Island from 2005 to 2011. The risk factors for 30-day mortality (patients

died within 30-day of cardiac surgery) along with short name and their numerical codes (where

necessary) are shown in Table 1.

Table 1: Long and short name of selected variables for cardiac surgery patients

Risk Factor (Variable) | Short Name |
Code |

Patient ID | ID | N/A |

Age | AGE | N/A |

Current smoking status | SMOKE | 0 for No, 1 for Yes |

Gender | SEX | 1 for Male; 0 for Female |

Urgency of procedure (surgery) | STAT | 0 for elective 1 for urgent 2 for emergency 3 for salvage |

Diabetic Status | DB | 0 for No; 1 for Yes |

Ejection fraction estimate (the % of blood emptied from the left ventricle at the end of the contraction) |
EFE | 0 for normal (>60%) 1 for mild (46-60%) 2 for moderate (30-45%) 3 for severe (<30%) |

Procedure (surgery) type | TP | 0 for CABG only 1 for Valve only 2 for CABG + Valve 3 for others |

Length of hospital stay | LOS | N/A |

Body mass index | BMI | N/A |

Mortality status | MORT | 0 for No; 1 for Yes |

Preoperative dialysis | DIAL | 0 for No; 1 for Yes |

Any blank/dot “cell” in the data file indicates missing value |

AssignmentTutorOnline

Note:

o 30-day mortality (MORT): patients who die within 30 days of cardiac surgery.

o Ejection fraction: the % of blood the left ventricular pump off in each beat of heart.

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Question 1 [25 marks]: Summarize the descriptive statistics for each of the variables listed in

Table 1 by mortality status and discuss the results. Note: Please do not copy and paste the SPSS

output; must summarize all the results in a single table in created in WORD (Hint: present list of

variables in Column 1 and summary statistics in subsequent columns).

Question 2 [2 marks]: Let us consider that a variable Y is heavily right skewed in the population. If you

draw a large sample from this population what should be the shape of this variable (Y) in the sample?

Justify your answer.

Question 3 [5 marks]: Consider that weight of tumor of bladder cancer patients in the population follows

normal distribution with a mean 50g and standard deviation 5g.

a) [2 mark] If a bladder cancer patient is selected randomly what is the probability that the tumor is

less than 45g?

b) [3 marks] If 4 of these patients are selected at random, calculate the probability that the average

weight of the 4 tumors (assume each patient has only one tumor) will be greater than 55g?

Question 4 [3 marks]: Juan makes a measurement in a chemistry laboratory and records the result in his

lab report. The standard deviation of the students’ lab measurement is 10 milligrams. Juan repeats the

measurement 4 times and records the mean of his 4 measurements.

a) [1 mark] What is the standard deviation of Juan’s mean result?

b) [2 marks] How many times must Juan repeat the measurement to reduce the standard deviation of

the sample mean to 2?

Question 5 [5 marks]: Suppose that in fact the blood cholesterol level of all men aged 20 to 30

is symmetric and bell shaped with mean 186 mg/dl and an unknown standard deviation.

a) [4 marks] Choose a simple random sample of 100 men from this population. The sample

standard deviation is 41 mg/dl.

1) What is the probability that the sample mean takes a value between 183 and 189

mg/dl?

2) What is the probability that the sample mean takes a value less than 191 mg/dl?

b) [1 marks] Choose a simple random sample of 1000 men from this population. Now what

is the probability that the sample mean falls within ±3 mg/dl of the population mean?

Question 6 [5 marks]: The age group to which Anne belongs has mean height 1.6 metre and

standard deviation 0.1 metre. The age group to which Devi belongs has mean height 1.2 metre

and standard deviation 0.08 metre. Anne is 1.7 metre tall. Devi is 1.36 metre tall. Which is the

taller for their age?

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Question 7 [5 marks]: Find the true answer(s) for the following questions (selection of any false

answer(s) for a question will result in zero marks):

(A) It is necessary to estimate the mean blood sugar level by drawing a sample from a large

population of diabetic patients. The accuracy of the estimate will depend on:

a. The mean sugar level in the population;

b. The population size;

c. The sample size;

d. The way the sample is selected;

e. The variance of sugar level in the population.

(B) The prevalence of a condition in a population is 0.1. If the prevalence is estimated

repeatedly from samples of size 10, these estimates will form a distribution which:

a. Is a sampling distribution;

b. Is approximately normal;

c. Has mean 0.1;

d. Have variance 0.001;

e. None of the above is true.

(C) If the size of a random sample is increased, we would expect:

a. The mean to decrease;

b. The standard error of the mean to decrease;

c. The standard deviation to decrease;

d. The sample variance to increase;

e. The mean to increase.

(D) The standard error of the mean of a sample:

a. Measures the variability of the observations;

b. Is the accuracy with which each observation is measured;

c. Is a measure of how far the sample mean is likely to be from the population mean;

d. Is a measure of how far the sample observations to be from the population mean;

e. Is less than the estimated standard deviation of the population.

(E) Diastolic blood pressure has a distribution which is slightly skew to the right. If the mean

and standard deviation were calculated for the diastolic blood pressures of a random

sample of men:

a. There would be fewer observations below the mean than above it;

b. The standard deviation would be approximately equal to the mean;

c. The majority of the observations would be more than one standard deviation from

the mean;

d. The standard deviation would estimate the accuracy of blood pressure

measurement;

e. About 95% of observations would be expected to be within two standard

deviations of the mean.

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