Q 8.139. - Elementary Statistics

Question

The Coruro's Burrow. The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to $600$ meters. Zoologists S. Begall and M. Gallardo studied the characteristics of the burrow systems of the subterranean coruro in central Chile and published their findings in the paper "Spalacopus cyanus (Rodentia: Octodontidac): An Extremist in Tunnel Constructing and Food Storing among Subterranean Mammals" (Journal of Zoology, Vol. 251. pp. $53-60$). A sample of $51$ burrows had the depths, in centimeters (cm), presented on the Weiss Stats site. Use the technology of your choice to do the following.

a. Obtain a normal probability plot. boxplot, histogram, and stem and leaf diagram of the data.

b. Based on your results from part (a), can you reasonably apply the $t-$interval procedure to the data? Explain your reasoning.

c. Find and interpret a $90\%$ confidence interval for the mean depth of all subterranean coruro burrows.

Step-by-Step Solution

Answer

Part (a) 

Leaf Unit $=0.10$

Stem Leaf

$$\begin{gathered} 1 08 2 \\ 2 09 7 \\ 2 10 \\ 4 11 08 \\ 12 12 01123588 \\ 16 13 3399 \\ 23 14 0245799 \\ \left(8\right) 15 00134689 \\ 20 16 002567789 \\ 11 17 24459 \\ 6 18 2389 \\ 2 19 37 \end{gathered}$$

Part (b) We can reasonably use the $t-$interval procedure for the data.

Part (c) The mean depth of all subterranean coruro's burrows, $\mu$ lies somewhere between $14.3470 \mathrm{cm}$ and $15.7549 \mathrm{cm}$.

Part (a) Step 1: Given information

The subterranean coruro is a social rodent that lives in vast colonies below in burrows that can be$600$ meters long. The depths of $51$ burrows were measured in centimeters (cm) and posted on the Weiss Stats website.

Part (a) Step 2: Explanation

Now, draw a probability plot for the given data.  

Now construct a box plot for a given data.  

Now construct the histogram for the given data. 

Part (a) Step 3: Explanation

Create a stem-and-leaf diagram for the supplied data set now.

DEPTH DISPLAY BY STOM AND LEAF

Leaf Unit $=0.10$

Stem Leaf

$$\begin{gathered} 1 08 2 \\ 2 09 7 \\ 2 10 \\ 4 11 08 \\ 12 12 01123588 \\ 16 13 3399 \\ 23 14 0245799 \\ \left(8\right) 15 00134689 \\ 20 16 002567789 \\ 11 17 24459 \\ 6 18 2389 \\ 2 19 37 \end{gathered}$$

Part (b) Step 1: Explanation

The sample size $n=51(>30)$ indicates that this is a large sample. We can see that there is no outlier in the sample data from the graphical representations. The normal probability plot also shows that the variable in question is normally distributed. As a result, we may safely utilize the $t-$interval function on the data.

Part (c) Step 1: Explanation

By utilizing MINITAB,

The $95\%$confidence interval for the population mean $\mu$ is $(14.3470,15.7549)$, implying that the mean depth of all underground coruro's burrows, $\mu$ is somewhere between $14.3470 \mathrm{cm}$ and $15.7549 \mathrm{cm}$ utilizing