10.3 Comparing Two Independent Population Proportions
- Page ID
- 36519
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Learning Objective:
In this section, you will:
• Apply hypothesis testing and calculate confidence intervals to real-world problems about two population proportions
When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:
- The two independent samples are simple random samples that are independent.
- The number of successes is at least five, and the number of failures is at least five, for each of the samples.
- Growing literature states that the population must be at least ten or 20 times the size of the sample. This keeps each population from being over-sampled and causing incorrect results.
Hypothesis testing of two population proportions from independent samples.
- Random Variable: 𝑝̂1 − 𝑝̂2 = the difference between the two estimated proportions
- Distribution: Normal distribution
Example 1a: Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. Test at a 1% level of significance.
- Null and Alternative Hypothesis
- Calculator Work
- Test Statistic and P-Value
- Conclusion about the null hypothesis
1
- Final conclusion that addresses the original claim
Example 1b: Using the date from 1a, construct the corresponding confidence interval estimate for the difference between the proportions of adult patient reactions to medication A and medication B. What does the result suggest about the two proportion?
Example 2: Researchers conducted a study of smartphone use among adults. A cell phone company claimed that iPhone smartphones are more popular with whites (non-Hispanic) than with African Americans. The results of the survey indicate that of the 232 African American cell phone owners randomly sampled, 5% have an iPhone. Of the 1,343 white cell phone owners randomly sampled, 10% own an iPhone. Test at the 5% level of significance. Is the proportion of white iPhone owners greater than the proportion of African American iPhone owners?
- Null and Alternative Hypothesis
- Calculator Work
- Test Statistic and P-Value
- Conclusion about the null hypothesis
2
178
- Final conclusion that addresses the original claim
- Test the above claim by constructing an appropriate confidence interval.
For more information and examples see online textbook OpenStax Introductory Statistics pages 579-584.
“Introduction to Statistics” by OpenStax, used is licensed under a Creative Commons Attribution License 4.0 license