Practicing Inference with Categorical Data

One- and Two-Proportion Inference

Reminder: Constructing Confidence Intervals

Reminder: The Hypothesis Testing Framework

Single Proportion versus Comparing Two Proportions

A Completed Hypothesis Test: Dating Apps

A Completed Hypothesis Test: Dating Apps

A Completed Hypothesis Test: Dating Apps

A Completed Hypothesis Test: Dating Apps

A Completed Hypothesis Test: Dating Apps

A Completed Hypothesis Test: Dating Apps

Conclusion in Context: The sample data provides significant evidence to suggest a difference in dating app performance.

A Completed Confidence Interval: Office Hours

Interpretation: We are 90% confident that the true difference in regular attendance proportions (virtual minus in-person) is between 2.77% and 22.47%, with virtual office hour attendance being more prevalent

Examples to Try

• The following slides contain several practice scenarios
• There are more than we'll be able to complete during this class meeting
• The examples include a mixture of:
• Single population proportion scenarios
• Comparison of two population proportions scenarios
• Questions best answered with a confidence interval
• Questions best answered with a hypothesis test
• Part of the challenge is determining which tool and which formula to apply — that's intentional

Practice: Streaming Subscription Rates

Scenario: A streaming service wants to estimate the proportion of its users who would be interested in subscribing to a premium ad-free plan. Out of 450 users surveyed, 135 reported interest. Construct a 95% confidence interval for the population proportion of users interested in this subscription.

Practice: Satisfactory Work-Life Balance

Scenario: A company is comparing satisfaction with work-life balance between remote and in-office employees. Out of 200 remote workers, 160 are satisfied; out of 220 in-office workers, 154 are satisfied. Does this data provide evidence that remote workers are more satisfied than their in-office counterparts?

Practice: Autonomous Drone Deliveries

Scenario: A city planning board wants to gauge public acceptance of autonomous delivery drones. They surveyed 1,000 random residents and 597 were supportive. Determine whether a majority of residents support the drone delivery initiative.

Practice: College Athletes and Vegan Diets

Scenario: A university athletic department is curious whether the proportion of athletes following a vegan diet differs between male and female athletes. Of 176 randomly sampled male athletes, 12 follow a vegan diet; of 153 female athletes, 28 follow a vegan diet. Do these samples provide evidence that the proportions differ?

Practice: Working in Your Field

Scenario: A career services department wants to compare the proportion of new graduates working in their field between those who completed internships and those who did not. Of 150 students who completed internships, 110 are working in their field; of 130 without internships, 82 are. Construct a 90% confidence interval for the difference in proportions.

Practice: Getting News from Social Media

Scenario: Researchers want to estimate the proportion of college students who use social media as their primary source of political news and determine if it exceeds 70%. Of 320 randomly selected students, 246 said they use social media as their primary news source. Test at α = 0.10.

Practice: Mobile Voting Apps

Scenario: A local government wants to estimate the proportion of residents in favor of adopting a mobile app for voting. Out of 500 residents surveyed, 127 expressed support. Construct a 99% confidence interval for the proportion in favor.

Practice: Support for a New Environmental Policy

Scenario: A politician claims that a minority of the public supports a new environmental policy. A random sample of 900 people finds that 54% of them support the policy. At the 5% significance level, can you reject the politician's claim?

Exit Ticket

Navigate to our MAT240 Exit Ticket Form, answer the questions, and complete the task below.

Note. Today’s discussion is listed as 14. Proportions and Comparing Proportions

Task: A study is being done to determine whether legalizing recreational marijuana has majority public support in the state of New Hampshire. In a random sample of 450 residents, 247 said they were in favor. Verify that the bounds for a 90% confidence interval for the true proportion of New Hampshire residents in favor of legalization are about 0.5102 and 0.5876. Interpret those bounds in the context of the scenario. What does your interval imply?

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