A researcher is interested in whether mother-calf pairs of humpback whales swim

Question

A researcher is interested in whether mother-calf pairs of humpback whales swim faster when they are joined by a male whale, who are physiologically able to swim more quickly than the young whale. They measure the swimming speed in miles of six mother whales who are travelling with calves before and after they are each joined by an adult male. On average, mother whales swam faster when a male whale was present, with SS=120 and MD=2.5. Is this a significant increase in swimming speed? Use a one tailed test with an alpha level of =0.05. Clearly label each of the 4 hypothesis testing steps, and interpret your findings!

Explanation / Answer

Step :

H0 : There is no differece in traveling speed with calves before and after thery are each joined by an adult male. 1 = 2

Ha = There is sigificant positive increase in traveling speed of feamles when joined with a male whale in comparison to when joined only by calves. 1 > 2

Step: II Significance level = 0.05

Step III: Test statistic

Here the SS (sum of squares) = 120

standard deviation of difference sd= sqrt[120/(n-1) = sqrt [120/5] = 4.89898

stanard error of difference = sd / sqrt(n) = 4.89898/6 = 0.8165

Mean Difference = 2.5

t = MD/ se0 = 2.5/0.8165 = 3.062

dF = 5 and alpha = 0.05  

tcr = t5, 0.05 = 2.015

so t > tcritical so we shall reject the null hypothesis.

Step : 4

here we can conclude that there is significant positive difference in speed for mother whales who are travelling each joined by an adult male than traveling with calves alone.

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