1) To estimate the average number of sick days in the Clinic for a given year, the survey is conducted.The employees are categorised into nurses, doctors and administrators. The sickness rate will vary, as the groups of employees have different work outlines and have different incomes. Therefore, stratified random sampling, is used with each group forming a separate strata in order to conduct survey. The no. of employees in the strata are given in table below:

Table-1:

Doctors 120

Nurses 80

Administrators 10

a.If 25 employees are required for survey, calculate the sample size from each stratum if proportional allocation is done.

b.Using the data from table 2, obtained from sampling 9 Doctors, 7 nurses and 4 administrators, to calculate the mean number of sick days for that year.

c.Place a 95% confidence bound on the mean.

d. Calculate the total number of sick days for the year.

e.Place a bound on the total number of sick days and interpret this bound.

Table-2:

Doctors (9) Nurses(7) Administrators(4)

8 4 5

7 8 12

Number 10 3 10

Of 12 12 11

Sick 19 7 -

Days 6 10 -

13 15 -

12 - -

9 - -

Mean 10.67 8.43 9.5

S 15.5 18.29 9.67

f. When a member of the above 3 teams get sick, it will cost the clinic a fixed $10,000, on top of this fixed cost, the cost of replacement of a Doctor would be $2000, replacing a nurse will cost $500 and replacing an administrator will cost $550. Calculate the mean cost of sick leave for the clinic.

g. Place a bound on the mean cost of sick leave for the clinic.

h. On the basis of fixed cost and the cost of sick leave for doctors, nurses and administrative staff given in part (f) (let us assume that the cost C = $33,700), calculate the size of stratified sample n that minimise the variance. Use this value of n to estimate the size of samples from individual strata (n₁ , n₂ and n₃) and then calculate minimum variance of the cost.

i. What would be the mean and variance of the total cost of sick leave per year for the clinic based on the information obtained in part (f) & (g)?

kindly provide detailed answer for every part from a to i with formulas. It should not be in excel