will be able to
· understand the purpose for using t-test and chi-square test .
· understand procedures for tests of hypotheses based on small samples.
· solve problems to test the hypotheses concerning mean(s) using t-distribution.
· solve problems to test the hypothesis whether the population has a particular variance using chi-square test.
· solve problems to test the hypotheses relating to independence of attributes and goodness of fit using chi-square test.

**TESTS BASED ON SAMPLING DISTRIBUTIONS I**

**W Gosset (1876-1937)**, born in England studied Chemistry and Mathematics** **at New College , Oxford. Upon graduating in 1899, he joined
a brewery in Ireland. Gosset applied his statistical knowledge both in the
brewery and on the farm to the selection of the best varieties of Barley.
Gosset acquired that knowledge by study, by trial and error, and by spending
two terms in 1906– 1907 in the biometrical laboratory of Karl Pearson. Gosset
and Pearson had a good relationship. Pearson helped Gosset with the mathematics
of his research papers. The brewery where he was employed allowed publishing
his work under a pseudonym (“Student”). Thus, his most noteworthy achievement
is now called Student's *t*, rather
than Gosset's, *t*-distribution.

The student will be
able to

·
understand the
purpose for using t-test and chi-square test .

·
understand procedures
for tests of hypotheses based on small samples.

·
solve problems to
test the hypotheses concerning mean(s) using t-distribution.

·
solve problems to
test the hypothesis whether the population has a particular variance using
chi-square test.

·
solve problems to
test the hypotheses relating to independence of attributes and goodness of fit
using chi-square test.

In the earlier chapter, we have discussed various problems related
to tests of significance based on large samples by applying the standard normal
distribution. However, if the sample size is small (*n* < 30) the
sampling distributions of test statistics are far from normal and the
procedures discussed in Chapter-1 cannot be applied, except the general
procedure. But in this case, there exists a probability distribution called *t*-distribution
which may be used instead of standard normal distribution to study the problems
based on small samples.

Tags : Tests Based on Sampling Distributions I , 12th Statistics : Chapter 2 : Tests Based on Sampling Distributions I

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12th Statistics : Chapter 2 : Tests Based on Sampling Distributions I : Introduction | Tests Based on Sampling Distributions I

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