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You are investigating the flight characteristics of different kinds of birds. You collect a sample of 33 European swallows (Hirundo rustica) and measure their air-speed velocity in a borrowed wind tunnel. You find the mean air-speed velocity to be 11 meters/second with a standard deviation of 3 meters/second. You then collect a sample of 37 African swallows (Hirundo spilodera) and repeat your experiment in the wind tunnel. This time, you measure a mean air-speed velocity of 12 meters per second with a standard deviation of 2 meters per second.
(a) At a 2% significance level, do you have sufficient evidence to support a claim that the African swallow flies faster, on average, than the European swallow? Explain your answer (don't just say yes or no).
(b) What is the p-value associated with your experimental outcome? Explain how you arrived at your answer, don't just write down a number.
(c) Find a 90% confidence interval for the mean difference between the airspeed velocity of an African swallow and that of the European swallow.
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