Sampling Distribution of a Proportion (Examples)

  1. Suppose that incumbents typically receive 57% of the vote in elections.

    1. What is the probability that in a random sample of 600 voters, less than 52% say they will vote for the incumbent?

    2. If you sampled 600 voters and found that 52% or less said they would vote for the incumbent, what is your opinion of the value of the population proportion in the problem?

  2. Suppose a pharmaceutical company claims that 98% of their prescription drugs contain the appropriate amount of the active ingredient. A sample of 750 servings (tablets) is measured and 720 of those have the correct amount of the active ingredient.

    1. What is the probability of observing a sample such as this or more extreme?

    2. What is your opinion about the claim of the company?

    3. After your analysis, the company changes and says that only 95% of the tablets contain the correct amount of the active ingredient. Do you agree?
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