Question: Go to StatKey and click on 'Test for a Single Proportion' under the 'Randomization Hypothesis Tests' tab. Using the data set 'Paul The Octopus (Correct

Go to StatKey and click on 'Test for a Single Proportion' under the 'Randomization Hypothesis Tests' tab. Using the data set 'Paul The Octopus (Correct Forecast)', generate 10000 samples by clicking on the 1000 choice ten times. This data set is a small sample of 'guesses' that an English-born, German-resident octopus named Paul had regarding football matches in several different tournaments around the world. Paul correctly picked the winner of eight different matches, a feat that no common octopus would likely do.

a. State the variable(s) of interest in the problem and whether they are quantitative or categorical.

b. Write the hypotheses in plain English.

c. Describe the parameter of interest using the correct notation.

d. Write the hypotheses using the parameter from (c).

e. Perform a hypothesis test at = 0.05. Does it show evidence Paul may actually be a psychic octopus?

f. Perform the hypothesis test again but this time using a normal approximation, giving the mean and standard deviation of the approximation.

g. Is your estimate from (f) justified? Explain.

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