"Instead of Reading This, Maybe You Should Take a Nap" reported in the New York Times that the United States ranked fairly high (eleventh) in an ACNielsen survey of countries around the world, in terms of what percentage of adults go to bed after midnight (34%); the highest percentage (75%) was found in Portugal, and the next highest (69%) in Taiwan.
a. The article does not mention sample sizes. Assume that 100 adults were
surveyed in Portugal and 100 in Taiwan. Construct a table of observed counts going to bed after midnight or not, along with a table of counts expected if overall proportions were the same in the two countries (rounding to the nearest tenth).
b. Calculate the chi-square statistic.
c. State whether your chi-square statistic is large, not large, or borderline.
d. State whether the P-value is small, not small, or borderline.
e. Tell whether or not there is a significant difference in proportions going to bed after midnight in the two countries.
f. Recall that if all counts in a table are multiplied by the same number, the resulting chi-square statistic is also multiplied by that number. Would the conclusions that you reached in part (e) still hold if only 50 were sampled in each country instead of 100?
g. Would the conclusions you reached in part (e) still hold if 1,000 each were sampled in Portugal and Taiwan, instead of 100 in each country?
h. The top five countries in terms of percentage of "night owls" were Portugal, Taiwan, South Korea, Hong Kong, and Spain. Discuss the potential role played by climate, and propose two possible ways to test if climate affects the percentage of night owls in a country, one in which the explanatory variable is quantitative and one in which it is categorical.