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Hypothesis test, population proportion

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A candidate must gather at least 8,000 valid signatures on a petition before the deadline in order to run in an election. One candidate turns in 10,000 signatures right before the deadline, but it's always expected that some percentage of them are invalid. Elections officials take the random sample of 100 signatures and thoroughly investigate them to find that 84% are valid. Is this statistically significant evidence that the candidate has enough valid signatures overall? Explain.

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This solution is a 336 word, step-by-step example showing how to perform a hypothesis test to evaluate a population proportion.

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Hypothesis Testing: Population proportion

Please explain how you obtained your results.

1. A student wants their College to offer Kickboxing classes as a Physical Education class. To justify that the class is desired he surveys 200 students and finds that 56% would be interested in taking the class. He goes to his Dean and tells him that based on his survey over half of the student body would be interested in taking the class.

a) State the null and alternative Hypotheses (H0 and H1).
b) Calculate the test statistic and the associated p-value.
c) What is the critical value for ?
d) State your conclusion (reject H0 or fail to reject H0 )and explain your reasoning.
e) Was the student's claim correct?

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