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Two Proportions quiz

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  • What is the null hypothesis (H0) when testing two population proportions?
    The null hypothesis is that the two proportions are equal, or p1 = p2.
  • How do you write the alternative hypothesis (Ha) if you are testing for any difference between two proportions?
    The alternative hypothesis is p1 ≠ p2, indicating a two-tailed test.
  • What is the formula for the test statistic (z) in a two-proportion hypothesis test?
    The formula is z = (p̂1 - p̂2) / sqrt[p̄q̄(1/n1 + 1/n2)], where p̄ is the pooled proportion.
  • How do you calculate the pooled proportion (p̄) for two samples?
    Add all successes from both samples and divide by the total number of trials: p̄ = (x1 + x2) / (n1 + n2).
  • What conditions must be checked before performing a two-proportion z-test?
    Each sample must be random and independent, and both must have at least 5 successes and 5 failures.
  • How do you calculate the sample proportions p̂1 and p̂2?
    Divide the number of successes by the sample size for each group: p̂1 = x1/n1 and p̂2 = x2/n2.
  • What does it mean if the p-value is greater than the significance level (alpha) in a two-proportion test?
    You fail to reject the null hypothesis, indicating there is not enough evidence of a difference.
  • How do you interpret a confidence interval for the difference in two proportions if it includes zero?
    If zero is within the interval, you fail to reject the null hypothesis, suggesting no significant difference.
  • What is the point estimate when constructing a confidence interval for two proportions?
    The point estimate is the difference in sample proportions: p̂1 - p̂2.
  • How is the margin of error (E) calculated for a confidence interval of two proportions?
    E = z* × sqrt[(p̂1q̂1/n1) + (p̂2q̂2/n2)], using individual sample proportions, not the pooled proportion.
  • What critical value (z*) do you use for a 90% confidence interval?
    The critical z value for a 90% confidence interval is 1.645.
  • When using a TI-84 calculator, which function is used for a two-proportion hypothesis test?
    Use the 2-PropZTest function on the TI-84 calculator.
  • What does it mean if the confidence interval for p1 - p2 does not include zero?
    It means there is enough evidence to suggest a significant difference between the two proportions.
  • How do you decide whether to reject the null hypothesis using the p-value?
    If the p-value is less than alpha, reject the null hypothesis; otherwise, fail to reject it.
  • What is the relationship between hypothesis testing and confidence intervals for two proportions?
    Both methods test for differences; if the confidence interval includes zero, you fail to reject H0, matching the hypothesis test result.