Exercises - Hypothesis Tests for Proportions (One Sample)

  1. In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won. Use a 0.01 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

    1. Identify the claim
    2. State the null and alternative hypotheses
    3. Check any relevant assumptions
    4. Find the value of the relevant test statistic
    5. Determine if this is a one-tailed or two-tailed test
    6. Identify the significance level
    7. Find any relevant critical value(s)
    8. Make a sketch of the relevant distribution, indicate the location of the rejection region, the test statistic, and any critical values for the test
    9. Find the p-value for the test
    10. Conclude whether or not to reject the null hypothesis
    11. Make an appropriate inference

  2. The Gallup Poll reported that 45% of individuals felt they were worse off than 1 year ago. A politician feels that this is too high for her district, so she commissions her own survey and finds that, out of 150 randomly selected citizens, 58 feel they are worse off today than 1 year ago. At significance level 0.05, is the politician correct about her district?

  3. Adults were randomly selected for a Newsweek poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 481 were in favor, 401 were opposed, and 120 were unsure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 120 subjects who said that they were unsure, and use a 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician's claim?