In a Study of Feeding Behavior, Zoologists Recorded the Number

question 90

Essay

In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the number of grunts and and the age of the warthog (in days)are listed below: $\begin{array}{cc}\hline \text { Number of Grunts } & \text { Age (days) } \\\hline 82 & 117 \\60 & 133 \\31 & 147 \\36 & 152 \\55 & 159 \\32 & 166 \\54 & 175 \\9 & 181 \\12 & 187 \\\hline\end{array}$

a. Write the equation of a straight-line model relating number of grunts $( y )$ to age $( x )$ .
b. Give the least squares prediction equation.
c. Give a practical interpretation of the value of $\hat { \beta } _ { 0 }$ , if possible.
d. Give a practical interpretation of the value of $\hat { \beta } _ { 1 }$ , if possible.

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Definitions:

Binomial Distribution

A probability distribution that summarizes the likelihood that a value will take one of two independent states under a given number of trials.

Sampling Distribution

Sampling Distribution is the probability distribution of a given statistic based on a random sample, used to make inferences about a population.

Sample Proportion

The ratio of members in a sample exhibiting a certain trait to the total number of members in the sample.

Central Limit Theorem

A principle stating that the distribution of sample means approaches a normal distribution as the sample size becomes larger, regardless of the population's distribution.