A random sample of 170 boys from 8502 boys in an area showed that 21 had some
nutritional deficiency. Estimate the proportion of nutritionally deficient boys and the
standard error of the estimate. Find the confidence interval also.
The proportion of nutritionally deficient boys is
p̂=21/170 = 0.1235.
The standard error
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An insurance company insured 1000 scooter drivers, 3000 car drivers and 6000 truck
drivers. The probabilities that the scooter, car and truck drivers meet with an
accident, are 0.02, 0.04 and 0.25, respectively. One of the insured driver meets with
an accident. What is the probability that he is a (i) car driver; (ii) truck driver?
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.
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 |
In a locality, 100 persons were randomly selected and asked about how far they had studied. The results are shown in table given below
|
| Middle School | High School | College |
| Male | 10 | 15 | 25 |
| Female | 25 | 10 | 15
|
A population of size 10000 is divided into 4 strata. Their sizes and standard
deviations are given below:
A stratified random sample of size 500 is to be drawn from this population.
Determine the sizes of samples from these strata, in case
i) Proportional allocation is used.
ii) Neyman’s optimum allocation is used.
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.
Calculate the 5-yearly moving average for the following data of the profits of a
company (in Rs. Lakhs) during 1995 to 2010:
.
