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# Bootstrap Interval for the Difference of Two Population Parameters

• Bootstrap methods assume that our sample is an SRS and will give trustworthy conclusions only if this condition is met.

• These methods make no assumptions about the distribution your data comes from.

• The Bootstrap Interval for the Difference of Two Population Means is an alternative to the two-sample $t$-interval when the guidelines for its use are not met (such as when the data is strongly skewed or has outliers with low sample size).

• The Bootstrap Interval for Two Population Proportions is an alternative to the two-large-sample $z$-interval when the guidelines for its use are not met (such as an insufficient number of successes and failures).
 Sample 1 Sample 2 Sample data goes here (enter numbers in columns): Number of Successes Sample Size Sample 1: Sample 2: Calculate Interval for a Difference of Two: Population Means Population Proportions Confidence Level: 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Number of Bootstrap Samples: 1000 5000 10,000 50,000 100,000 500,000 1,000,000

 Sample Sizes: $n_1=$ $n_2=$ Sample Means: $\overline{x}_1=$ $\overline{x}_2=$ Sample Difference: $\overline{x}_1-\overline{x}_2=$ Confidence Interval for the Difference of Means: Sample Proportions: $\hat{p}_1=$ $\hat{p}_2=$ Sample Difference: $\hat{p}_1-\hat{p}_2=$ Confidence Interval for the Difference of Proportions:

 Frequency Sample 1 and Sample 2 Data Bootstrap Differences $\delta^*$ Shifted Bootstrap Differences $\delta^*+\overline{x}_1-\overline{x}_2$