Write three advantages and three limitations of systematic sampling
Systematic sampling is one in which the initial unit of sample is selected at random from the initial stratum of the universe and the other units are selected at a certain space interval from the universe arranged in a systematic order
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Calculate the 5-yearly moving average for the following data of the profits of a
company (in Rs. Lakhs) during 1995 to 2010:
.
In a binomial distribution, the probability of success is
p = 2 / 5. Calculate the
probability that (5)
the number of successes in n = 6 trails is at least 3.
the number of successes in n = 6 trails is 5.
State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.
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.
If the random variable X is normally distributed with mean 80 and standard deviation
5, then find (i) P[60.5 < X < 90], and (ii) P[X _ 80 < 1].
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.
