There are three children in a room, age 3, 4, and 5. What will happen to the mean and variance of the ages if a 4-year-old child enters the room? 0 The mean age will stay the same, but the variance will increase. O The mean age will stay the same, but the variance will decrease. O The mean age and variance will stay the same. O The mean age and variance will increase. Question 9 (1 point) Bird species from temperate regions must cope with relativer short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The following scatterplot displays this relationship, after taking the logarithm of each variable: 1.5 . \"3'. I . _ . . = . . a . E 0 v t u U c ' ' n O . . . I 5 us - . - _ ' I .1 ID 0 In . ' a I! . i n c u E ' . . . . g It . : I I: ' o ' ' ' . . a 5 0D I ' " 'I :3": '- o E o . 3' I :' . n g 415- .: a . : O 1.0 - o 1.5 0.0 0.2 0.4 0. B 0.3 1.0 1.2 log at Go ration ofegn laying {mum} Suppose the measurements were switched so that logarithm of testosterone level was treated as an explanatory variable rather than a response variable. What impact would this switch have on the correlation? O The correlation would switch signs. 0 The correlation would not make sense because logarithm of egg-laying duration is the explanatory variable. 0 The correlation would have a completely different magnitude. 0 The correlation would remain unchanged. Question 10 (1 point) Consider the following scatterplot of two variables X and Y: 10 04 07 10 15 25 30 What can be concluded from this scatterplot? The correlation between X and Y must be near 1 since there is a near- perfect relationship between them. O The correlation between X and Y must be close to - 1 since there is near- perfect relationship between them, but it is not a straight-line relationship. O The correlation between X and Y is close to 0, because the relationship is not linear. O The correlation between X and Y could be any number between -1 and +1, because there is not a straight-line relationship. Question 11 (1 point) Which of the following statements about correlation coefficients is TRUE? The correlation coefficient equals the proportion of times two variables lie on a straight line. O The correlation coefficient will be +1.0 only if all the data lie on a perfectly horizontal straight line. O The correlation coefficient measures the fraction of outliers that appear in a scatterplot. O The correlation coefficient is a unitless number and must always lie between -1.0 and +1.0, inclusive. Please use this information to answer questions 12 through 15: Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/1), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/1, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows