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Suppose that you have in your possession bivariate data giving birthrate and life expectancy information for a random sample of 15 countries. For each of the countries, the data give both x, the number of births per one thousand people in the country's population. and y, the country's A female life expectancy in years. The least-squares regression equation computed from your data is y = 79.49 .49x. Suppose that you're predicting the female life expectancy for a country whose birthrate is 31.5 births per one thousand people. You've used the regression equation to make your prediction, and now you're interested in both a prediction interval for this female life expectancy and a condence interval for the mean female life expectancy for countries with this same birthrate. Suppose that you've computed the following from the data. 0 mean square error (MSEJI \"a.\" 14.09 1 (315?)2 o E + 15 % 0.0?28, where x1, x2, ..., '5 denote the birthrates in the sample, and ; denotes their mean Based on this information, and assuming that the Egression assumptions hold, answer the questions below. (If necessary, consult a list of formulas.) (a) What is the 90% prediction interval for an individual value for female life expectancy (in years) when the birthrate is 31.5 births per 1000 people? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.) Lower limit: D Upper limit: I] (b) Consider (but do not actually compute) the 90% condence interval for the mean female life expectancy when the birthrate is 31.5 births per 1000 people. How would the prediction interval computed above compare to this condence interval [assuming that both intervals are computed from the same sample data)? O The prediction interval would be positioned to the right of the condence interval. 0 The prediction interval would have the same center as, but would be wider than, the condence interval. 0 The prediction interval would have the same center as, but would be narrower than, the condence interval. 0 The prediction interval would be positioned to the left of the condence interval. 0 The prediction interval would be identical to the condence interval. {c} For the birthrate values in this sample, 63.0 births per 1000 people is more extreme than 31.5 births per 1000 people is, that is, 63.0 is farther from the sample mean birthrate than 31.5 is. How would the 90% prediction interval for the mean female life expectancy when the birthrate is 63.0 births per 1000 people compare to the 90% prediction interval for the mean female life expectancy when the birthrate is 31.5 births per 1000 people? 0 The interval computed from a birthrate of 63.0 births per 1000 people would be narrower and have a different center. 0 The interval computed from a birthrate of 63.0 births per 1000 people would be narrower but have the same center. 0 The interval computed from a birthrate of 63.0 births per 1000 people would be wider and have a different center. 0 The interval computed from a birthrate of 63.0 births per 1000 people would be wider but have the same center. 0 The intervals would be identical