Biostatisitcs Exercise

1.Suppose it is known that in a certain population 10 percent of the population is colour blind. If a random sample of 25 people is drawn from this population, find the probability that

a) five or fewer will be colour blind

b) six or more will be colour blind

c) between six and nine will be colour blind

d) two, three or four will be colour blind

2.Suppose that 24 percent of a certain population have blood group A. for a sample of 25 people drawn from this population, find the probability that

a) Exactly three will have group A

b) Three  or more will have group A

c) Fewer than three will have group A

d) Exactly five will have group A

3. A hospital administrator, who has been studying daily emergency admissions over a period of several years, has concluded that they are distributed according to the poisson law. Hospital records reveal that emergency admissions have averaged three per day during this period. Find the probability that

a. exactly two emergency admissions will occur on a given day.

b. no emergency admission will occur on a given day.

c. either three or four emergency cases will be admitted on a given day.

4. If the mean number of serious accidents per year in a large factory (where the number of employees remain constant ) is five, find the probability that in the current year there will be

a. exactly seven accidents.

b. ten or more accidents.

c. No accidents.

d. Fewer than five accidents.

5. If the total cholesterol value for a certain population is approximately normally distributed with a mean of 200mg/100ml. And a standard deviation of 20mg/100ml. Find the probability that an individual picked at random from this population will have a cholesterol value

a. Between 180 and 200mg/100ml.

b. Greater than 225mg/100ml.

c. Less than 150mg/100ml.

d. Between 190 and 210mg/100ml

6. Average wt of baby at birth is 3.05 kg with the sd of 0.39 kg. if the birth wts follow normal distribution will you take

a. wt of 3.9 kg as abnormal?

b. wt of 2.5 kg as normal?

7. Menstrual cycle in women following normal distribution has mean of 28 days and sd of 2 days. How frequently would you expect a menstrual cycle of

a. more than 30 days?

b. less than 20 days?

8. A researcher was interested to determine if  urine levels of a certain chemical in pre-term infants with late metabolic acidosis and pre-term infants without the condition differs. The mean, s. d. and sample sizes are as follows:

Sample	n	Mean	S
With condition	35	8.5	5.5
Without condition	40	4.8	3.6

9. A health researcher wants to estimate the mean hb level in the community. Preliminary information is that this mean is about 150 mg/l with sd of 32 mg/l. if a difference of up to 5 mg/l in either side in the estimate can be tolerated, how many subjects should be included in the study?

10. An intervention programme for tobacco users is to be implemented in certain community. Find the required sample size when the proportion of tobacco user in the community is reported to be 20% by some other study and a difference of upto 3 in either side is tolerable.

11. In a length of hospitalization study conducted by several cooperating hospitals, a random sample of 64 peptic ulcer patients was drawn from a list of all peptic ulcer patients ever admitted to the participating hospitals and the length of  hospitalization per admission was determined for each. The mean length of stay was found to be 8.25 days. If the population s. d. is known to be 3 days, can it be concluded that the mean hospital stay is more than 7 days, less than 9 days and different than 7 days.

In the above problem, if population SD is not known and sample SD is 3 days and sample size is 25 records of patients, solve for all three conditions.

12. Protoporphyrin levels were measured in two samples of subjects. Sample 1 consisted of 50 adult male alcoholics with ringed sideroblasts in the bone marrow. Sample 2 consisted of 40 apparently healthy non alcoholic males.

Can we conclude that protopophyrin levels are higher in alcoholic population than in non alcoholic?

The mean and SD were

Sample	Mean	SD	Sample number
1	340	250	50
2	45	25	40

In the above problem if SDs are sample SDs and sample sizes are 22 for both samples apply t test for unequal variances and equal variances

13. Researchers wish to know if the data they have collected provide sufficient evidence to indicate a difference in mean serum uric acid levels between normal individuals and individuals with mongolism at 5% level. The data are as follows:

Sample	n	Mean
Mongoloids	12	4.5 mg/100ml
Normal individuals	15	3.4 mg/100ml

a)            Let the populatiom s. d. for both is 1, solve using z test.

b)            Let the sample s. d. for both is 1,  assume equality of variances and solve. Assume unequal variances and solve.

14. Can we conclude that chronically ill children tend on average, to be less self confident than healthy children? A test designed to measure self confidence was administered to 32 chronically ill and 32 healthy children. The mean scores and s. d. were as follows.

	Mean	S
Ill group	22.5	4.1
Well group	26.9	3.2

 

15. A group of 350 adults who participated in a health survey were asked whether or not they were on diet. The responses by sex are as follows:

	Sex
	Male	Female	Total
On diet	14	25	39
Not on diet	159	152	311
Total	173	177	350

Do these data suggest that being on diet is dependent on sex? Let a =. 05

16. A sample of 500 college students participated in a study designed to evaluate the level of college students’ knowledge of a certain group of common diseases. The following table shows the students classified by major field of study and level of knowledge of group of diseases.

	Knowledge of disease
Major field	Good	Poor		Total
Premedical	31	91		122
Other	19	359		378
Total	50	450		500

17. A study of 190 pregnancies yielded the following results on the relationship between hypertension of mother and a certain complication of pregnancy.

                                                                     Mother hypertensive

A certain complication of pregnancy	Yes	No	Total
Present	23	55	78
Absent	12	100	112
Total	35	155	190

Do these data suggest that the two conditions are not independent?

18. Determine if there is association between scabies amongst the school children and the socio economic status.

	Socio economic status
Scabies status	I	II	III	IV	V	Total
With scabies	23	127	640	806	63	1659
Without scabies	427	1573	7560	7526	541	17627
Total	450	1700	8200	8332	604	19286

Posted in: Biostatistics,Exercise