Question

A species of bird has beaklengths which are normally distributed and believed to have an average of 4.2 centimeters. A simple random sample of 5 birds on one particular island has the following beaklengths: 4.25, 4.31, 4.18, 4.36, and 4.4. Do an appropriate hypothesis test to decide whether the birds on this island have an average beaklength which is different than 4.2 centimeters.

Answer 1

We make the computations here as:

X	X - Mean(X)	(X - Mean(X))^2
4.25	-0.05	0.0025
4.31	0.01	1E-04
4.18	-0.12	0.0144
4.36	0.06	0.0036
4.4	0.1	0.01
21.5		0.0306

The sample mean and sample standard deviation here are computed as:

As we are testing here whether the mean is different from 4.2, therefore this is a two tailed test. The test statistic here is computed as:

For n - 1 = 4 degrees of freedom, we get the p-value from the t distribution tables for two tailed test here as:

p = 2P( t4 > 2.5565) =  2*0.0314 = 0.0628

As the p-value here is 0.0628 > 0.05 but < 0.1, therefore the test is significant at 10% level of significance, but not at 5% level of significance. Therefore only at 10% level of significance, we can conclude here that the mean of the population is different from 4.2