Herpetologists found that a certain species of python have an average length of 20.5 feet with a standard deviation of 2.3 feet which is normally distributed. The scientists collect a random sample of 30 adult pythons and measure their lengths. The average length in the sample is found to be 19.5 feet. One of our herpetologists fears pollution may be affecting the natural growth of the pythons. Do you think the sample result is unusually small? Explain. Test this claim at 0.05 level of significance.

a. State the null and alternative hypotheses with appropriate notation.

b. In the context of this problem, describe a Type I error.

c. In the context of this problem, describe a Type II error.

d. Using the sample data given, decide if a hypothesis test can be conducted.

e. Using your calculator list here all important information from conducting the appropriate hypothesis test; for instance, examples might include the p-val, critical value, test statistic, etc. Draw a conclusion based on this information.

f. Restate the conclusion you drew in part e. in the context of the question.