Question

An online magic 8 ball has 20 response options, 5 of which are neutral. An instructor claims that the responses are all equally likely to occur and that the proportion of neutral responses is .25. A student is skeptical of this claim, believing that neutral responses are less likely. The student queries the magic 8 ball 50 times and gets 9 neutral responses. Is there convincing evidence that less than 25% of responses are neutral? What are the appropriate hypotheses for this test?

Answer 1

`H_0:p=0.25`

`H_a: p<0.25`

Explanation:

We know that the null hypothesis is the statement which show that there is no statistical difference between two groups tested.

The alternative hypothesis is the statement which is exactly opposite to the null hypothesis . i.e. it shows that there is statistical difference.

According to the given question, we have

Null hypothesis :
`H_0:p=0.25`

Alternative hypothesis :
`H_a: p<0.25`

Hence, the appropriate hypotheses for this test :

`H_0:p=0.25`

`H_a: p<0.25`