The test of significance for the large samples can be explained by the following assumptions:
TESTING OF HYPOTHESIS
Test of Significance for Large Samples
The test of significance for the large samples can be explained by the
1. The random sampling distribution
of statistics is approximately normal.
2. Sampling values are sufficiently
close to the population value and can be used for the calculation of standard
error of estimate.
Standard Error Of Mean.
In the case of large samples,
when we are testing the significance of statistic, the concept of standard
error is used. It measures only sampling errors. Sampling errors are involved
in estimating a population parameter from a sample, instead of including all
the essential information in the population.
standard deviation of the population is known, the formula is
The standard error of the mean, σp = Standard deviation of the
population, and n = Number of observations in the sample.
standard deviation of population is not known, we have to use the
standard deviation of the sample in calculating standard error of mean.
The formula is
Standard deviation of the sample, and n = Sample size
Illustration: A sample of 100 students from
Pondicherry University was taken and their average was found to be 116 lbs with
a standard deviation of 20 lbs. Could the mean weight of students in the
population be 125 pounds? Solution:
us take the hypothesis that there is no significant difference between the
sample mean and the hypothetical population mean.
Since, the difference is more
than 2.58 S.E.(1% level) it could not have arisen due to fluctuations of
sampling. Hence the mean weight of students in the population could not be 125
Significance For Small Samples If the sample size is less than
30, then those samples may be regarded as small samples. As a rule, the methods
and the theory of large samples are
not applicable to the small samples. The small samples are used in testing a given hypothesis, to find out the
observed values, which could have arisen by sampling fluctuations from some
values given in advance. In a small sample, the investigator’s estimate will
vary widely from sample to sample. An inference drawn from a smaller sample
result is less precise than the inference drawn from a large sample result. t-distribution will be employed,
when the sample size is 30 or less and the population standard deviation is
formula isIllustration: The following results are
obtained from a sample of 20 boxes of mangoes: Mean
weight of contents = 490gms, Standard
deviation of the weight = 9 gms. Could the sample come from a population having a mean of 500 gms? Solution:The computed value is less than the table value.
Hence, our null hypothesis is accepted.
Tags : Research Methodology - Statistical Analysis
Last 30 days 1440 views