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The length of an adult dwarf seahorse (hippocampus zosterae) is normally distributed with a standard deviation...

The length of an adult dwarf seahorse (hippocampus zosterae) is normally distributed with a standard deviation of 1.25 mm. A marine biologist claims that the population mean length is less than 23 mm. They select 95 adult dwarf seahorses at random, and calculate their mean length to be 22.6 mm. Test the marine biologist’s claim at a 5% significance level.

a) Define the parameter and random variable of interest.

b) State the null and alternative hypotheses, and identify the claim.

c) Determine the distribution of the test statistic. (Check the relevant criteria.)

d) Calculate the test statistic.

e) Find the p-value.

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