Question: Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.

Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?

i: What is the null hypothesis?

ii: What is the alternate hypothesis?

iii: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?

iv: Is this a directional or nondirectional test?

v: What is the test statistic?

vi: What is the p-value?

vii: What is your conclusion?

viii: Is it possible that an error was committed? If so, which kind?

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