A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below:
| Centre | m | Patients seen | |||
| 1 | 4 | 1 | 2 | 6 | 3 |
| 2 | 4 | 4 | 3 | 2 | 2 |
| 3 | 4 | 5 | 3 | 2 | 1 |
| 4 | 4 | 4 | 1 | 5 | 6 |
| 5 | 4 | 2 | 3 | 4 | 7 |
Estimate the average number of daily patients per paramedic from all the 25 centres. Also estimate the relative efficiency of the estimator used with respect to the usual sample mean estimator.
To estimate the average number of daily patients per paramedic from all 25 centers, we will use the Horvitz-Thompson estimator, a statistical technique commonly used in survey sampling. This estimator provides a consistent and unbiased estimate of the population total or mean based on a simple random sample without replacement.
First, we calculate the average number of patients for the selected sample of 5 centers:
(4 + 6 + 2 + 3 + 4) / 5 = 19 / 5 = 3.8 patients per paramedic on average for the
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A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below:
| Centre | m | Patients seen | |||
| 1 | 4 | 1 | 2 | 6 | 3 |
| 2 | 4 | 4 | 3 | 2 | 2 |
| 3 | 4 | 5 | 3 | 2 | 1 |
| 4 | 4 | 4 | 1 | 5 | 6 |
| 5 | 4 | 2 | 3 | 4 | 7 |
The monthly income (in Rs. Lakhs) of five employees in a company are as follows:
25, 20, 30, 15, 10. (i) List all possible samples (without replacement) of size 2 (ii)
Compute the mean of all samples and set up the sampling distribution of sample
mean.
1000 students at college level were graded according to their IQ levels and the economic condition of their parents, as follow:
| Economic condition | IQ level | ||
| High | Low | Total | |
| Rich | 230 | 170 | 400 |
| Poor | 230 | 130 | 600 |
|
Total | 700 | 300 | 1000 |
Does each of the following statements pertain to an estimate or an estimator? If the
statement pertains to an estimate is it an interval estimate or point estimate? If the
statement pertains to an estimator write the estimator.
i) The head of a publishing company says that the firm’s physics textbook will sell
about 9000 copies in 2012.
ii) A cencus prefers the median to the mean as a measure of central tendency for the
income distribution of families in a standard metropolitan city.
iii) A stock market analyst who appears on the television programme, estimates that
the price of a particular common stock will be between 50 and 60 at the end of
six months
A company appointed four salesman A, B, C and D and observed their sales in three
seasons – Summer, Winter and Monsoon. Test whether the average sales of the four
salesmen differ in amount (in Rs. Lakhs) as given below by one-way analysis of
variance (ANOVA) using observations after taking deviation from 30.
The frequency distribution of marks of 230 students in a statistics paper in a class is given below:
Class Interval Frequency
10 – 20 12
20 – 30 30
30 – 40 ?
40 – 50 65
50 – 60 ?
60 – 70 25
70 – 80 18
Total 230
Given that the median value of distribution is 46, determine the missing frequencies.
There are 1000 pages in a book out of which 100 pages are defective. What is the
probability that out of first 50 pages 10 pages will be defective?