Chapter 6: Inference For Categorical Data Flashcards
What is the point estimate for a population proportion?
The sample proportion, denoted as p̂.
What is the formula for standard error of a sample proportion?
SE = sqrt[p(1 - p) / n] or use p̂ if p is unknown.
What conditions must be met to use inference for proportions?
Independence and at least 10 successes and 10 failures.
How do you calculate a 95% confidence interval for a proportion?
p̂ ± 1.96 × SE
What is the purpose of a confidence interval?
To estimate a range of plausible values for a population parameter.
What is the null hypothesis in a test for one proportion?
H₀: p = p₀
What is the formula for the Z-test statistic for one proportion?
Z = (p̂ - p₀) / SE
What does the p-value represent in hypothesis testing?
The probability of observing the data if the null hypothesis is true.
When do you use a pooled proportion?
When testing if two population proportions are equal (H₀: p₁ = p₂).
What is the pooled proportion formula?
p̂ = (x₁ + x₂) / (n₁ + n₂)
What is the formula for SE when comparing two proportions?
SE = sqrt[p̂₁(1 - p̂₁)/n₁ + p̂₂(1 - p̂₂)/n₂]
What are the conditions for comparing two proportions?
Independence within and between groups, ≥10 successes/failures in each group.
How do you determine the required sample size for a desired margin of error?
Use the formula n ≥ (z* × sqrt[p(1-p)] / ME)²
Why use p̂ = 0.5 for sample size estimation?
It gives the most conservative (largest) estimate.
What is the Chi-square test used for?
Testing whether observed categorical data match expected frequencies.
What is the Chi-square statistic formula?
χ² = Σ[(O - E)² / E]
What is the null hypothesis in a Chi-square goodness-of-fit test?
That the observed counts match the expected distribution.
What are degrees of freedom in a GOF test?
Number of categories minus 1.
What does a large Chi-square statistic indicate?
A large difference between observed and expected counts.
What should you check before using the Chi-square test?
All expected counts should be at least 5.
