82. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally repre- sentative online poll of 2,015 American adults aged 18 and above. They found that $$ 3.3 \% $$ of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the United States and India? A 2014 survey conducted by the Registrar General of India found that $$ 29 \% $$ of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a $$ 99 \% $$ confidence interval for the difference in proportions of vege- tarians in India and the United States. (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain.

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The $$ 99\% $$ confidence interval for the difference in vegetarian proportions between India and the U.S. is approximately $$ (-0.2954, -0.2186) $$, indicating a significantly higher proportion of vegetarians in India. This suggests we would reject the null hypothesis in a two-sided test, supporting the alternative that the proportion of vegetarians in India is higher than in the U.S.

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