91Ó°ÊÓ

Cottonmouth Litter Size. In the article "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. $29$ No. $3$ pp. $391-398$), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of $44$ female cottonmouths yielded the following data on the number of young per litter.

a. Use the data to obtain a point estimate for the mean number of young per litter, $\mathrm{μ}$ of all female eastern cottonmouths. (Note: $\left.\mathrm{Î\pounds }{x}_i=334.\right)$

b. Is your point estimate in part (a) likely to equal $\mathrm{μ}$ exactly? Explain your answer.

Step by step solution

01

Part (a) Step 1: Given information

5	12	7	7	6	8	12	9	7
4	9	6	12	7	5	6	10	3
10	8	8	12	5	6	10	11	3
8	4	5	7	6	11	7	6	8
8	14	8	7	11	7	5	4

02

Part (a) Step 2: Concept

The formula used: Sample mean$=\frac{1}{n}×\underset{i=1}{\overset{44}{∑}}{x}_i$

03

Part (a) Step 3: Calculation

Here the sample size is 44 i.e., $n=44$

Let $x_i$be the $i-th$sample observation on number of young per litter. $i=1,2……,44$

Here $\underset{i=1}{\overset{44}{∑}}{x}_i=334$

$∴$Sample mean $=\frac{1}{n}×\underset{i=1}{\overset{44}{∑}}{x}_i$

$$\begin{gathered} =\frac{1}{44}×334 \\ =7.59 \end{gathered}$$

Mean no of young per litter is $8$(approximately)

$∴$the point estimate of the population means $=8$

The estimated value of mean no. of young per litter for the population is $7$

04

Part (b) Step 1: Explanation

No, it's doubtful that the sample mean $\stackrel{¯}{x}$ will be exactly the same as the population mean $\mathrm{μ}$ We're attempting to guess (estimate) the population mean value solely by drawing a sample, or a subset of the population. As a result, some sampling error is unavoidable.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!