Question

For each of the given​ situations, write out the alternative​ hypothesis, being sure to state whether it is​ one-sided or​ two-sided.a) A consumer magazine discovered that 30​% of a certain computer model had warranty problems over the first three months. From a random​ sample, the manufacturer wants to know if a new model has improved that rate.Complete the alternative hypothesis and determine whether the alternative hypothesis is one-sided or two-sided.

Answer 1

Null hypothesis:
`p\leq 0.3`

Alternative hypothesis:
`p > 0.3`

Explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is
`p>0.3` since we want to check if the new model has improved the warranty rate, we can express it like this:

`p-0.3<0` since are equivalent expressions.

And the alternative hypothesis should be the complement:

Null hypothesis:
`p\leq 0.3` or
`p=0.3`

So the correct system of hypothesis for this case would be:

Null hypothesis:
`p\leq 0.3`

Alternative hypothesis:
`p > 0.3`

The alternative way should be:

Null hypothesis:
`p = 0.3`

Alternative hypothesis:
`p > 0.3`