Testing if p1-p2 = 0.19, calculate the test statistic, z, where p^1 = 0.74 sampled from 75, and p^2 = 0.44 sampled from 82.

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**Hypothesis Testing for Proportions**

In this scenario, we are testing if the difference between two proportions, \( p_1 - p_2 \), is equal to 0.19. We need to calculate the test statistic \( z \).

**Given:**
- \( \hat{p_1} = 0.74 \) (Sample proportion 1), sampled from a sample size of 75.
- \( \hat{p_2} = 0.44 \) (Sample proportion 2), sampled from a sample size of 82.

**Objective:**
Calculate the test statistic \( z \) to determine whether the observed difference between the sample proportions is significantly different from the hypothesized difference of 0.19. 

This involves using the formula for the test statistic for the difference between two population proportions. The standard error and other relevant calculations can be made to complete the test.

Note: Determine the test statistic by employing the formula for two-proportion z-test in statistical analysis.
Transcribed Image Text:**Hypothesis Testing for Proportions** In this scenario, we are testing if the difference between two proportions, \( p_1 - p_2 \), is equal to 0.19. We need to calculate the test statistic \( z \). **Given:** - \( \hat{p_1} = 0.74 \) (Sample proportion 1), sampled from a sample size of 75. - \( \hat{p_2} = 0.44 \) (Sample proportion 2), sampled from a sample size of 82. **Objective:** Calculate the test statistic \( z \) to determine whether the observed difference between the sample proportions is significantly different from the hypothesized difference of 0.19. This involves using the formula for the test statistic for the difference between two population proportions. The standard error and other relevant calculations can be made to complete the test. Note: Determine the test statistic by employing the formula for two-proportion z-test in statistical analysis.
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