# Significance Levels, P-Values, and Confidence Intervals

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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...nce 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).

Null hypothesis:

H0: µ1 = µ2

H0: There is no significant different between the European and African swallows.

Alternative hypothesis:

Ha: µ1 ≠ µ2

Ha: There is a significant different between the European and African swallows.

Critical value:

'Z' at α = 0.02 level of significance (two-tailed test) is given by

= =2.33 (by referring normal distribution table)

Test Statistic:

Since both the sample sizes n1 = 33 and n2 = 37 are greater than 30, we can use the large sample test Z-test to test the ...