Additional Exercises The question of atheism was asked by WIN-Gallup International in a similar survey that was conducted in 2005.T Table 4 summarizes the results from the 2005 and 2012 surveys. Exercise 14 Answer the following two questions using the inference function. (a) Is there convincing evidence that Spain has seen a change in its atheism index between 2005 and 2012? Hint: Create a new dataset for respondents from Spain. Then use their responses as the first input on the inference , and use year as the grouping variable. (b) Is there convincing evidence that the United States has seen a change in its atheism index between 2005 and 2012? Exercise 15 If in fact there has been no change in the atheism index in the countries listed in Table 4, in how many of those countries would you expect to detect a change (at a significance level of 0.05) simply by chance? Exercise 16 Suppose you're hired by the local government to estimate the proportion of residents that attend a religious service on a weekly basis. According to the guidelines, the estimate, at 95% confidence level, must have a margin of error of no greater than 3%. You have no idea what to expect for p. How many people would you have to sample to ensure that you are within the guidelines? Hint: You do not need to use the dataset to answer this