1. Hypothesis testing

2. • Hypothesis-
*A tentative explanation for an observation, phenomenon, or scientific
problem that can be tested by further investigation.
*Something taken to be true for the purpose of argument or
investigation; an assumption.
*An educated guess based on observation.
Eg: Avogadro’s hypothesis
Theory- Explain a large class of observations through a model and
have predictive capability which can be tested
Eg: Einstein’s theory of relativity
Law- Generalizes a body of observations
-A statement of fact meant to describe, in concise terms, an action
or set of actions. It is generally accepted to be true and universal
Eg: Newton’s Law of gravitation

3. • Null hypothesis: the assumption we wish to
test Ho
• Alternate hypothesis : when we reject the null
hypothesis
• Type 1 error: Rejecting a null hypothesis when
it is in fact true
• Type 2 error: Accepting a null hypothesis
when it is false

4. • The roofing contract for a sports complex
requires the roofing sheets to be 0.04 inches
thick. The sports complex samples a lot of 100
sheets from a supply of 10,000 sheets and finds
the sample mean is 0.0408 inches. From past
experience it is known that these sheets come
from a thickness population with standard
deviation of 0.004 inches. On the basis of the
sample data the sports complex must decide
whether or not to accept the consignment of
10,000 sheets

5. • The basic question is, “if the true mean is 0.04
what are the chances of getting a sample with
a mean thickness of 0.0408?”
If the probability of getting such a sample is very
low, then we must conclude that the true
mean is not really 0.04

6. • Calculate standard error of the mean
• Calculate z=2
• So probability of the sample mean being less
than 0.0392 or larger than 0.0408 is 4.5%

7. • A manufacturer supplies axles for trucks. These
axles must be able to withstand a 80000 psi in
stress tests, but an excessively strong axle will
increase production costs. A sample of 100 axles
from production has a mean strength of 79600
psi. Experience indicates that the standard
deviation of the strength of the axles is 4000 psi.
If the axle manufacturer uses a significance of 0.05,
should he accept the axles?

8. • Ho- The axles are from a population with a
mean of 80,000
• H1- The true mean is not 80,000