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, role="math" localid="1650465230449" $61$landed in the mud, and role="math" localid="1650465221489" $11$landed on the rocks. Carry out a chi-square goodness-of-fit test. What do you conclude?

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.

The null and alternative hypotheses are:

$H0:p1=0.56,$

$H0:p2=0.29,$

$H0:p3=0.15$

H_{localid="1650465424047" $\alpha$}: At least one of pi is different

Following is the calculation of test statistics

The test statistics is

localid="1650618645139" $$\begin{gathered} {\chi }^2=\sum (O-E{)}^2/E \\ =14.4742 \end{gathered}$$

We can compute the degree of freedom as follow:

localid="1650618876773" $$\begin{gathered} Degreeoffreedom=Numberofcategories-1 \\ =3-1 \\ =2 \end{gathered}$$