Q.8 - The Practice of Statistics for AP

Question

Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of $56$% sand, $29$% mud, and $15$% rocks. The biologists chose $200$ seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, $128$seagulls landed on the sand, $61$ landed in the mud, and $11$landed on the rocks. Carry out a chi-square goodness-of-fit test. What do you conclude?

Step-by-Step Solution

Answer

Using the chi-square table, the $p$-value for the second degree of freedom is $0.000719$. The $p-$value is below the level of significance. The null hypothesis is found to be false. There is enough data to conclude that seagulls have a preference for landing locations.

Step 1: Given Information

Biologists conducted a study in an enclosed outdoor environment with a section of beach made up of $56$ percent sand, $29$ percent muck, and $15$ percent rocks, according to the query. The biologists randomly selected $200$ seagulls. Each seagull was released into the open air on its own and watched until it landed on a patch of beach. There were $128$ seagulls on the sand, 61 in the mud, and $11$on the rocks in total. Each seagull was released into the free air and observed until it landed on a beach patch. In total, $128$ seagulls landed on sand, $61$ on mud, and $11$ on rocks. 

Step 2: Explanation

The null and alternative hypotheses are:

$H0: p1=0.56,$

$H0: p2=0.29,$

$H0: p3=0.15$

H_$\alpha$: At least one of pi is different

Following is the calculation of test statistics

The test statistics is

$$\begin{gathered} {\chi }^2=\sum (O-E{)}^2/E \\ =14.4742 \end{gathered}$$

We can compute the degree of freedom as follow:

$$\begin{gathered} Degree of freedom=Number of categories-1 \\ =3-1 \\ =2 \end{gathered}$$