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Disclaimer: Homework assignment must be done cleanly in A4 size papers, must be stapled (if extends more than one sheet of paper). Solutions and answers must be written in complete sentences Hand writing should be readable. Maximum mark 25% No late homework will be accepted. 1. The birth weights(Kilogram) of 30 children were recorded as follows 2.0, 4.0, 3.1, 2.1, 2.3, 3.0, 2.3, 3.5, 2.6, 3.0, 4.2, 2.8, 3.1, 3.7, 2.9, 2.7, 3.2, 3.5, 2.8, 2.7, 4.1, 3.5, 2.5, 3.9, 3.1, 2.7, 2.8, 3.7, 3.8, 2.2 (a) Construct grouped frequency distribution. (b) Draw frequency polygon , histogram and ogive curve. (c) Calculate Arithmetic mean and standard deviation. (d) Calculate median value and mode value. 2. A total of 20 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results were summarized below Class-Limit A-B C - 17 E-F G-H 30 - I K-L Class-Boundary Number of people LCF 7 4 MCF 20 18 16 Class Mark 18 Then, (a) Complete the above table (b) Calculate Mean and Median (c) Draw histogram, a frequency polygon , and a less than ogive for the above table. 3. In an insurance company study of the causes of 1000 deaths, the following data were obtained Cause of death Heart disease Cancer Stroke Accidents Other No of Deaths 432 217 93 34 224 Construct a pie chart to represent the data 4. The mean and standard deviation of the distribution of the weights of a group of 100 patients are found to be 40 kgs and 10 kgs respectively. If at the time of calculation two observations were wrongly taken as 30 kg and 70 kg in place of 3 kg and 27 kg respectively, find the correct standard deviation. 5. The median and mode of the patient waiting time at hospital to visit a doctor are 33.5 minutes and 34 minutes respectively. Minute 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Total Frequency 4 16 F1 F2 F3 6 4 230 Determine the missing frequencies, and compute the arithmetic mean. 6. A hospital collected data on the age group of each of 120 people that were treated as outpatients on a particular day. the results are summarized below Age group Number of people pre-school school 60 and above others 18 24 35 43 Draw a appropriate bar chart to illustrate these results 7. A student received an A in Basic writing skills (3 credits), a C in Human Physiology (3 credits), a B in Biochemistry (4 credits), and a D in Medical Microbiology (2 credits). Assuming A=4 grade points, B=3 grade points, C=2 grade points, D=1 grade point, and F=0 grade points, find the student’s grade point average. 8. Gadise obtained results of 63 in Biostatistics and 58 in Biochemistry. For Biostatistics the class mean was 58 and the standard deviation 3.4, and for Biochemistry the class mean was 55 and the standard deviation 2.3. Compared to the rest of the class did Gadise do better in Biostatistics or Biochemistry? 9. A dietitian is interested in comparing the sodium content of real cheese with the sodium content of a cheese substitute. The data for two random samples are shown. Real cheese 310 220 420 240 45 180 Cheese Substitute 40 90 270 130 180 260 250 340 290 310 Compute coefficient of variation and interpret it. 10. The combined mean of 50 students who passed and failed in Biostatistics is 51.6. If the number of students who passed is 40 and its mean is 59.25. Find out the mean marks of the students who failed? 11. A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of common colds. A survey of 450 people provided the following information: Daily amount of vitamin C taken None 500 mg 1000 mg No colds 57 26 17 At least one cold 223 84 43 Is there evidence of a relationship between catching a cold and taking vitamin C? 12. Ten persons came into contact with a person infected with tuberculosis. The probability of being infected after contacting a person with tuberculosis is 0.1. (a) What is the probability that nobody is infected? (b) What is the probability that at least 2 persons are infected? Page 2 (c) What is the expected number of infected persons? 13. A general practitioner doctor is interested in knowing how many years her patients stay with her. Let X = the number of years a patient will stay with the doctor. Over the years, she has established the following probability distribution: x 1 2 3 4 5 6 7 P (X = x) 0.1 0.2 0.1 K 2K 0.2 0.1 (a) Find the value K, E (x) and Var (x) 14. Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24. (a) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL? (b) What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL? 15. A box contains 24 bottles of pills , 4 of which are defective. If 4 are sold at random, find thefollowing probabilities. (a) Exactly 2 are defective. (b) None is defective. (c) All are defective. (d) At least 1 is defective. 16. A drug company is testing a new drug which is supposed to reduce blood pressure. From the six people who are used as subjects, it is found that the average drop in blood pressure is 2.28 points, with a standard deviation of .95 points. (a) What is the 95% confidence interval for the mean change in pressure? 17. Several studies have shown that women with many children are less likely to get ovarian cancer. In a new study, data are collected from 25 women ages 40-49 with ovarian cancer. The mean parity (number of children) of these women is 1.8 with standard deviation 1.2. Suppose the mean number of children among women in the general population in this age group is 2.5. (a) What test can be used to test the hypothesis that women with ovarian cancer have fewer children than women in the general population in the same age group? (b) Perform the test (c) Identify the critical region(s) (d) What do you conclude from this study? (e) What are the type I and type II errors for this question? Page 3