Question

A publisher reports that 76v% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 200200 found that 70p% of the readers owned a personal computer. State the null and alternative hypotheses.

Answer 1

Answer:

Null Hypothesis: 'The proportion of readers who own a personal computer is not 76%'

Alternative hypothesis: 'The proportion of readers who own a personal computer is not 76%', or it could also be stated as 'The proportion of readers who own a personal computer is less than 76%'

Step-by-step explanation:

A null hypothesis is an experimental statement that negates the existence of a relationship between two phenomena that are measured, or it is a statement that tells of no association between two experimental groups. The experimenter sets out to test the null hypothesis with a bid to disprove or accept the null hypothesis after subjecting experimental results through various confidence tests.

The null hypothesis is generally accepted to be true, unless it is proven otherwise, and it always comes from the point of negation between the associated phenomena. It is denoted commonly by the symbol 'H₀'.

The null hypothesis is analogous to the statement that ' a person is assumed to be innocent,  (null hypothesis is assumed to be true) unless proven guilty beyond all reasonable doubt ' (and it is rejected only if the results show a statistically significant difference between what is measured and what is stated in the null hypothesis).

When the null hypothesis is rejected, it is replaced by the alternative hypothesis, a statement that holds true to the observed result and rejects the null hypothesis.

In this example, the proposition on ground was that 76% of readers of a publication, has a personal computer, the null hypothesis comes to negate this association/claim, that it is not a 76% proportion, but it could be more or less than 76%, hence the statement 'The proportion of readers who own a personal computer is not 76%'. Upon carrying out the research, it was found that the actual value was 70%, hence the null hypothesis is not rejected, and the null hypothesis is still the alternative hypothesis which can also be stated as 'The proportion of readers who own a personal computer is less than 76%', or in the exact words of the null hypothesis.