11F Preview

Preparing for the next class

In the next in-class activity, you will need to be able to distinguish between situations that require a one-sample test of proportions or a two-sample test of proportions and set up the hypotheses for a two-sample test of proportions.

As you have seen in previous activities, a one-sample test of proportions tests a claim about a population proportion. A two-sample test of proportions tests a claim about two population proportions.

Questions 1–4: These questions will ask you to distinguish between situations where a one-sample test would be appropriate and where a two-sample test would be appropriate. For these questions, consider whether there is one population under consideration or whether you need to test a claim that compares two populations. When testing a claim that compares two populations, you must also check that the two populations are independent.

Question 1

An engineer is developing a new method for manufacturing a certain piece of equipment. Safety regulations state that no more than 0.5% of items produced can be defective. In order to test the claim that the manufacturing process meets the regulations, which test is needed?

  1. a) One-sample test of proportions
  2. b) Two-sample test of proportions

Question 2

A researcher is studying the effectiveness of a vaccine to protect against a certain disease and has conducted an experiment where one group of subjects has been given the vaccine and one group has not. The researcher wants to test the claim that vaccinated people contract the disease at a lower rate than unvaccinated people. Which test is needed?

  1. a) One-sample test of proportions
  2. b) Two-sample test of proportions

Question 3

Suppose a researcher wants to test the claim that the proportion of self-identified Democrats who use NBC News as their main source of political news is different from the proportion of self-identified Republicans who do. Which test is needed?[1]

  1. a) One-sample test of proportions
  2. b) Two-sample test of proportions

Question 4

A study found that 66.8% of adults in Norway have talked in their sleep at some point during their lives. Which test is needed to test the claim that more than 65% of Norwegian adults have talked in their sleep?[2]

  1. a) One-sample test of proportions
  2. b) Two-sample test of proportions

Question 5

The null and alternative hypotheses for a two-sample test both involve a comparison of proportions associated with two populations. We use [latex]p_{1}[/latex] to denote the true proportion in one population under consideration and [latex]p_{2}[/latex] to denote the true proportion in the other population.

 

  1. Part A: The null hypothesis is that there is no difference between the two population proportions. Which of the following expresses the null hypothesis, [latex]H_{0}[/latex]?
    1. a) [latex]p_{1} = p_{2}[/latex]
    2. b) [latex]p_{1} \neq p_{2}[/latex]
    3. c) [latex]p_{1} > p_{2}[/latex]
    4. d) [latex]p_{1} < p_{2}[/latex]
  2. Part B: Which of the following is equivalent to your answer in Part A?
    1. a) [latex]p_{1} - p_{2} > 0[/latex]
    2. b) [latex]p_{1} - p_{2} < 0[/latex]
    3. c) [latex]p_{1} - p_{2} = 0[/latex]
    4. d) [latex]p_{1} - p_{2} \neq 0[/latex]
      Hint: Subtract [latex]p_{1}[/latex] from both sides of the equation or inequality you chose in Part A.
  3. Part C: Suppose a researcher is studying the effectiveness of a vaccine to protect against a certain disease and has conducted an experiment where one group of subjects has been given the vaccine and one group has not. The researcher wants to test the claim that vaccinated people contract the disease at a lower rate than unvaccinated people. If p1 represents the proportion of vaccinated subjects who subsequently contract the disease and p2 represents the proportion of unvaccinated subjects who subsequently contract the disease, which of the following expresses the alternative hypothesis, HA?
    1. a) [latex]p_{1} = p_{2}[/latex]
    2. b) [latex]p_{1} \neq p_{2}[/latex]
    3. c) [latex]p_{1} > p_{2}[/latex]
    4. d) [latex]p_{1} < p_{2}[/latex]
  4. Part D: Which of the following is equivalent to your answer in Part C?
    1. [latex]p_{1} - p_{2} > 0[/latex]
    2. b) [latex]p_{1} - p_{2} < 0[/latex]
    3. c) [latex]p_{1} - p_{2} = 0[/latex]
    4. d) [latex]p_{1} - p_{2} \neq 0[/latex]

    Hint: Subtract [latex]p_{2}[/latex] from both sides of the equation or inequality you chose in Part C.

  5. Part E: Suppose a researcher wants to test the claim that the proportion of self-identified Democrats who use NBC News as their main source of political news is different from the proportion of self-identified Republicans who do. If p1 is the proportion of Democrats and p2 is the proportion of Republicans who use NBC News as their main source of political news, which of the following expresses the alternative hypothesis, HA?
    1. a) [latex]p_{1} - p_{2} > 0[/latex]
    2. b) [latex]p_{1} - p_{2} < 0[/latex]
    3. c) [latex]p_{1} - p_{2} = 0[/latex]
    4. d) [latex]p_{1} - p_{2} \neq 0[/latex]
  6. Part F: Which of the following is equivalent to your answer in Part E?
    1. a) [latex]p_{1} - p_{2} > 0[/latex]
    2. b) [latex]p_{1} - p_{2} < 0[/latex]
    3. c) [latex]p_{1} - p_{2} = 0[/latex]
    4. d) [latex]p_{1} - p_{2} \neq 0[/latex]

 

  1. Grieco, E. (2020, April 1). Americans’ main sources for political news vary by party and age. Pew Research Center. https://www.pewresearch.org/fact-tank/2020/04/01/americans-main-sources-for-political-news-vary-by-party-and-age/ ↵
  2. Bjorvatn, B., Gronli, J., & Pallesen, S. (2010, December). Prevalence of different parasomnias in the general population. Sleep Med, 11(10), 1031-1034. https://pubmed.ncbi.nlm.nih.gov/21093361/ ↵