Question

A newsletter publisher believes that above 78 % of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to
substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario.

Answer 1

Answer:

$h_{0}$: p= .78

$h_{a}$: p > .78

Step-by-step explanation:

Determining the null and alternate hypotheses of a scenario require several components. The first is if one should use p or mu. This depends on if they are assessing a proportion or a mean, since the publisher states a percentage, you know that they are asking for a proportion, and therefore should use p. Next, they will need to assess what value to use for the hypothesis statements, here only .78 is provided and therefore should be used in both. Finally, it is time to add in the comparison symbols, the null hypothesis always uses an equals sign so it therefore becomes:

$h_{0}$: p= .78

The alternate hypothesis then needs to consider if the researchers claim that the new proportion is greater, fewer, or different. In this case it is greater as they think that the ownership is above 78%, so a greater than sign would be used and the final statement would be:

$h_{a}$: p > .78