Question

The class Polyplacophora includes about 500 species of mollusks called chitons. Chitons live in shallow water along rocky shores. The West Indian chiton, C. olivaceus , is quite variable in color and is often difficult to identify to species. A malacologist recently found an odd colored population of chitons and wanted to determine whether they were C. olivaceus. It is well known that the width to length ratio in C. olivaceus has a median of 0.65. Below are ratios for 13 of the odd colored specimen.

0.75 0.73 0.67 0.69 0.64 0.66 0.71 0.79 0.73 0.68 0.69 0.63 0.70  

Is their ratio significantly different from C. olivaceus? Carry out an appropriate test and give all of the statistical calculations and reach a conclusion in the context of the setting.

Answer 1

The class Polyplacophora includes about 500 species of mollusks called chitons. Chitons live in shallow water along rocky shores. The West Indian chiton, C. olivaceus , is quite variable in color and is often difficult to identify to species. A malacologist recently found an odd colored population of chitons and wanted to determine whether they were C. olivaceus. It is well known that the width to length ratio in C. olivaceus has a median of 0.65. Below are ratios for 13 of the odd colored specimen.

0.75 0.73 0.67 0.69 0.64 0.66 0.71 0.79 0.73 0.68 0.69 0.63 0.70  

Is their ratio significantly different from C. olivaceus? Carry out an appropriate test and give all of the statistical calculations and reach a conclusion in the context of the setting.

Single sample t test used

Two tailed test

=3.8426                

Table value of t with 12 DF at 0.05 level =2.1788

Rejection Region: Reject Ho if t < -2.1788 or t > 2.1788

Calculated t = 3.8426 falls in the rejection region

The null hypothesis is rejected.

There is enough evidence to support that the ratio significantly different from C. olivaceus.

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0.65
Level of Significance	0.05
Sample Size	13
Sample Mean	0.6977
Sample Standard Deviation	0.0448
Intermediate Calculations
Standard Error of the Mean	0.0124
Degrees of Freedom	12
t Test Statistic	3.8426
Two-Tail Test
Lower Critical Value	-2.1788
Upper Critical Value	2.1788
p-Value	0.0023
Reject the null hypothesis