Assignment no 4 (2015-2016) 80m

Faculty:Mr. Mohammed Hanif Semester:VI Department:BME

Subject: BS

Question no 1

a) Sample variances are computed for tidal volumes (ml) of 2 groups of patients suffering

From atrial septal defect. The results and samples sizes were as follows:

n1=31, s12=35,000 and n2=41, s2

2=20,000 compute 95% confidence interval for ratio of

2 population variances.( Given F.975(30,40)= 1.94 and F.025= .4975) 2m

b) compute 90% confidence interval for ratio of 2 population variances? 2m

c) compute 98% confidence interval for ratio of 2 population variances 2m

d) compute 95% confidence interval for ratio of 2 population variances 2m

e) A sample of 16 ten years old girls had a mean of weight of 71.5 ponds with a SD of 12

Ponds respectively. Assuming normality find 90% confidence interval for true

Population mean 2m

f) find 95% confidence interval for true Population mean 2m

g) find 98% confidence interval for true Population mean 2m

h) find 99% confidence interval for true Population mean 2m

i) Write general equation for Confidence interval for difference between sample mean and

population mean for small sample? 2m

j) Write general equation for Confidence interval for difference between 2 sample mean

For small sample? 2m

Question no 2 a) Researchers data collected is sufficient to indicate a difference in mean of serum uric

Acid levels between normal & down syndrome subjects. The data consists of uric

Acid readings of 12 and 15 with down syndrome and normal subjects and mean of

4.5mg/100ml and 3.4 mg/100ml respectively. Is there is a difference between means

Between down syndrome and normal subjects.? 6m

b) Researchers wish to know of 2 populations differ with respect to the mean value

Of total serum complement activity (CH50). the data consists of CH50 determinations

Of n2=20 apparently normal subjects and n1=10 subjects with disease. The sample

Means are 62.6 and 47.2 for disease and normal respectively and SD’s are 33.8

and 10.1 for disease and normal respectively. 6m

c) The 16 control subjects made a mean score of 11.53 on the evaluation with a

SD of 3.681. Construct 90%, 95% and 98% confidence interval for true

Population mean. 8m

Question no 3

a) Explain properties of Chi-square in details. 6m

b) The face sheet of patients record maintained in a local health department contain

10 entries. A sample of 100 records revealed the following distribution of erroneous

Entries:

No of erroneous entries out of 10 No of records

0 8

1 25

2 32

3 24

4 10

5 or more 1

Total 100

Test the goodness of fit of these data to binomial distribution with p=0.2 6m

c) Given the following tabe:

Boys →

Fathers↓

Intelligent Boy Unintelligent Boy Total

Skilled Father 24 12 36

UnSkilled Father 32 32 64

Total 56 44 100

Do these support the hypothesis that skilled father have intelligent boys? Use ᵪ2

Test 8m

Question no 4

a) During one semester a student received grades in various subjects as shown in table.

Test at the 0.01 level whether there is any significant difference in his grades

In there subjects. (given : F.99 (3,12)= 5.95)

Math 72 80 83 75

Science 81 74 77 80

English 88 82 90 87

Economics 74 71 77 70

6m

b) Seeds of 4 different types of corn are planted in 5 blocks. Test at 0.01 level whether

The yields in bushel per acre , as shown in the following table vary significantly

With soil differences (i.e 5 blocks) (given F.99(4,12)=5.41)

Types of corn →

Blocks↓

1 2 3 4

A 12 15 10 14

B 15 19 12 11

C 14 18 15 12

D 11 16 12 16

E 16 17 11 14

6m

c) There are 3 main brands of medicines. A set of its 120 sales is examined and found

to be allocated among 4 groups A,B,C,D and company names I,II and III shown in

table:

Groups →

Companies↓

A B C D

I 0 4 8 15

II 5 8 13 6

III 18 19 11 13

Is there any siginificant difference in company preferences ? Answer at 5% LOS using one

way ANOVA table.(take 10 as the code value to subtract from all given values in your

Working ) given [ F(3,8)0.05= 8.85 ] 8m