Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then ado

Question

Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. But the potential host birds lay eggs of different sizes. Does the cuckoo change the size of her eggs for different foster species? Below are the summary statistics for the mean length of the cuckoo eggs (in mm) between sparrow hosts and wagtail hosts.

                              WAGTAIL     SPARROW

SAMPLE SIZE         12                    22

MEAN                        21.999            23.336

STANDARD DEV.    1.037           0.859

a) USING THE POOLED TWO-SAMPLE T-METHODS, calculate the standard error of the distribution of differences in sample means. Round your answer to two decimal places.

b) Again, USING THE POOLED TWO-SAMPLE T-METHODS, what is the degrees of freedom for the t-statistic. (You do NOT have to calculate the t-statistic.)

Explanation / Answer

pooled sample variance (sp2) = ((n1 - 1)s12 + (n2 - 1)s22)/(n1 + n2 - 2)

                                       = (11 * (1.037)^2 + 21 * (0.859)^2)/(12 + 22 - 2)

                                       = 0.85

The standard error = sqrt(sp2/n1 + sp2/n2)

                              = sqrt(0.85/12 + 0.85/22)

                              = 0.33

b) Degrees of freedom = 12 + 22 - 2 = 32

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