7.11 Topic 11: Inference for Two Proportions 88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep- resentative online poll of 2,015 American adults aged 18 and over. 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 US 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 tarians in India and the US. vege- (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain. 89. It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data. User Nonuser Prefer new product Prefer standard product 19 31 29 27 (a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent. (b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain. 90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100 adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than 40 years old found that 59 purchased popcorn. (a) State the hypotheses for determining of there is a difference in the proportion of adults who purchase popcorn in each age group. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State your conclusion. (f) Would a confidence interval for the difference in proportions contain zero? Explain without constructing the interval. 91. Africa and the Middle East are two of the least popular regions traveled to in study abroad programs. Suppose a random sample of 250 college students found that 10 traveled to Africa for study abroad. A second random sample of 375 college students found that 10 studied in the Middle East. Is there evidence that more students study abroad in Africa than the Middle East? Perform the appropriate test and include all steps.