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A researcher wants to see whether a person's astrological sign is related to their personality. First, they ask a series of questions and use them to make a prediction about what sign they are likely to have and then see if the prediction matches the actual sign. Since there are 12 astrological signs, the prediction would be correct 1/12 of the time if guessing at random. Out of 846 interviews, the correct sign was predicted 76 times. Test the claim that the prediction is more accurate than random guessing at the =.05 level.

a. Write the null and alternative hypothesis.

b. Find the p-value. Round to 3 decimal places.

c. What can you conclude?