A study was conducted to determine if taller people earn more money over their career than shorter people. Using data collected from 2245 individuals from various careers, the researchers computed the correlation between average earnings over the past decade and height. The results are given in the table to the right. Occupation Correlation (r) Sample Size (n) Sales 0.43 117 Managers 0.34 453 Blue Collar 0.34 347 Service 0.29 267 Professional 0.29 451 Clerical 0.25 360 Forepersons 0.27 250 a. Interpret the value of r for forepersons. Choose the correct answer below. A. There is a fairly weak positive linear relationship between height and average earnings over the last decade for forepersons. B. There is a fairly weak negative linear relationship between height and average earnings over the last decade for forepersons. C. There is a fairly strong positive linear relationship between height and average earnings over the last decade for forepersons.
Added by Patrick S.
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According to the given data, the correlation coefficient (r) for forepersons is 0.27. Now, we need to interpret the value of r. The correlation coefficient ranges from -1 to 1. A value of 0 indicates no linear relationship, while a value close to 1 indicates a Show more…
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Data on dating A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms. Then she measures the next man each woman dates. Here are the data (heights in inches): (a) Make a scatterplot of these data. Based on the scatterplot, do you expect the correlation to be positive or negative? Near $\pm 1$ or not? (b) Find the correlation $r$ step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for $r .$ Do the data show that taller women tend to date taller men?
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Scatterplots and Correlation
In a 2016 article titled "A Century of Trends in Adult Human Height," researchers reanalyzed 1472 population studies of more than 18.6 million participants worldwide between 1896 and 1996. They report that "The largest gain in adult height over the past century has occurred in South Korean women and Iranian men, who became 20.2 cm (95% confidence interval 17.5–22.7) and 16.5 cm (13.3–19.7) taller, respectively." What is the best conclusion about the change in height of South Korean women? Reference: NCD Risk Factor Collaboration (NCD-RisC). A Century of Trends in Adult Human Height. July 26, 2016. eLife Sciences. Retrieved from: https://elifesciences.org/content/5/e13410ent Which of the following is a valid conclusion? 1. We are 95% confident South Korean women have gained 19.7 cm, the most in height from 1896 to 1996. 2. We are 95% confident that our sample of South Korean women from 1896 and 1996 will have a difference in sample means between 17.5 cm to 22.7 cm. 3. We are 95% confident that basset hounds in 1896 were 17.5 cm taller on average and in 1996 are 22.7 cm taller on average. 4. We are 95% confident that South Korean women in 1996 are between 17.5 cm to 22.7 cm taller than South Korean women in 1896.
Madhur L.
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