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# Bootstrap Test 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 Test for Two Population Means is an alternative to the two-sample $t$-test 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 Test for Two Population Proportions is an alternative to the two-large-sample $z$-test 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: Test for a Difference of Two: Population Means Population Proportions $H_0: \mu$$\mu_0$ $H_a:\mu$ $\neq$ $\lt$ $\gt$ $\mu_0$ Level of Significance: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 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: $\overline{x}_1-\overline{x}_2=$ Sample Proportions: $\hat{p}_1=$ $\hat{p}_2=$ Sample Difference: $\hat{p}_1-\hat{p}_2=$ Lower Critical Value: $\delta_{L}^*=$ Upper Critical Value: $\delta_{U}^*=$ $p\mbox{-value}$:

 Frequency Sample 1 and Sample 2 Data Bootstrap Differences $\delta^*$