In a random sample of 100 persons taken from village A, 60 are found to be consuming tea. In another sample of 200 persons taken from a village B, 100 persons are found to be consuming tea. Do the data reveal significant difference between the two villages so far as the habit of taking tea is concerned?

To determine if there is a significant difference between the two villages regarding the habit of consuming tea, we can perform a hypothesis test for the difference between two proportions. Here’s the step-by-step procedure:

1. **Define the null and alternative hypotheses:**

   - \( H_0 \): \( p_1 = p_2 \) (There is no significant difference in the proportions of tea consumers in the two villages)
   - \( H_A \): \( p_1 \neq p_2 \) (There is a significant difference in the proportions of tea consumers in the two villages)

2. **Calculate the sample proportions:**

   - For village A: \( \hat{p}_1 = \frac{60}{100} = 0.60 \)
   - For village B: \( \hat{p}_2 = \frac{100}{200} = 0.50 \)

3. **Calculate the pooled sample proportion:**

   \[
   \hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{60 + 100}{100 + 200} = \frac{160}{300} = 0.533

Explore whether there is a significant difference in tea consumption between two villages using hypothesis testing. Sample data from village A (60 out of 100) and village B (100 out of 200) are analyzed. Learn step-by-step calculations and conclusions for statistical significance.

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