A set of 312 small wild birds caught at random was found to be
composed of 102 males (M), having sample mean wing length = 12.5 cm, with a standard deviation of 0.81 cm, and 210 females (F), with sample mean wing length 11.75 cm, and a standard deviation of, 0.74 cm. We propose to use this data to find out whether there is a difference between the male and female birds wing lengths.

(a) Establish the null, and alternative hypotheses. Find the estimated standard error, ESE, for the sampling distribution.

(b) Find the two sample test statistics, Z, associated with M, and, F.

(c) Do you accept or reject the null hypothesis at the 10%, significance level?