Question

7 A potential buyer of electric bulbs bought 100 bulbs each of two famous brands A and B. Upon
testing both these samples, he found that brand A had a mean life of 1500 hours with a standard
deviation of 50 hours whereas brand B had an average life of 1530 hours with a standard deviation
of 60 hours. Can it be concluded at 5% level of significance that the two brands differ significantly
in quality? (stansered value of Z=1.95)​

Answer 1

Answer:

A statistical hypothesis is an assumption about any aspect of a population. It could be the

parameters of a distribution like mean of normal distribution, describing the population, the

parameters of two or more populations, correlation or association between two or more

characteristics of a population like age and height etc.

Hypothesis is an integral part of any research or investigation. Many a time, initially

experiments or investigations are carried out to test a hypothesis, and the ultimate decisions are

taken on the basis of the collected information and the result of the test.

To test any statistical hypothesis on the basis of a random sample of n observations, we

divide the n- dimensional sample space into two regions. If the observed sample

point , falls into a region called critical or rejection region, the hypothesis is

rejected, but if the sample falls into complementary region, the hypothesis is accepted. The

complementary region is called acceptance region.

We can respect the various possibilities in decision making about a population from a

sample with the help of the following figure.

Decision

Hypothesis

Accept

TRUE FALSE

Right Decision Type-II Error

Reject Type-II Error Right Decision

Null hypothesis

A type of hypothesis used in statistics that proposes that no statistical significance exists

in a set of given observations. The null hypothesis attempts to show that no variation exists

between variables, or that a single variable is no different than zero. It is presumed to be true