Question

According to the Wildlife Service there is a 10% chance that a wolf will howl when the moon light intensity falls to or below 30cd/m. A group of zoologist in Lisbon thinks that the chance is much higher than 10%. In order to conduct a preliminary study they consider a small pack of wolves with 32 wolves in their sample. Answer the following questions.

(c)   To test the zoologists claim, set up proper null and alternative hypotheses. State relevant assumptions.

(d)   At 5% level of significance, what is the rejection region of the test?

(e)   What is the conclusion of the test? Specify the p-value.

Answer 1

a) The null and alternative hypotheses are :

against

d) Let denotes the sample proportion of wolves that will howl when the moon light intensity falls to or below 30cd/m.

Here

sample size n = 32 is given, but is not given.

d) At 5% level of significance,

The rejection region of the test :

e) Since is not given, it not possible to compute test statistic and p-value.

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if p-value < 0.05

where p-value = where z_obs is observed value of the test statistic.