Standard Deviation Correlation

STAT 1401, Fall 2023, Quiz 4. Instructions: Select the correct response. Use (E) for none of these. 1. The continuous measurements X and Y are to be taken on the individual in a population. The average of the values X −  X Y −  Y  over all individuals in the population is the population ___, where  X and  Y are respectively the population means of the distributions of X and Y. (A) correlation (B) covariance (C) variance (D) standard deviation 2. The measurements X is to be taken on the individual in a population. The average of the values X −  X  2 over all individuals in the population is the population ___, where  X is the population means of the distribution of X. (A) correlation (B) covariance (C) variance (D) standard deviation X− Y− X Y 3. The average of the values over all individuals in the population is the X Y population ___, where  X and  Y are respectively the population standard deviations of the distributions of X and Y. (A) correlation (B) covariance (C) variance (D) standard deviation 4. The principal square root of the population variance is the population ___. (A) correlation (B) covariance (C) variance (D) standard deviation 5. The (bivariate) X, Y measurements X 1 , Y 1 , … , X n , Y n  are to be taken on a sample of n individuals from the population. The statistic X 1 − XY 1 − Y  X 2 − XY 2 − Y … X n − XY n − Y S X,Y  n−1 is called the sample ____. ((A) correlation (B) covariance (C) variance (D) standard deviation 6. (continuation) The sample ____ is the statistic defined by S r  X,Y , SXSY where S X and S Y are respectively the sample standard deviations of the X’s and the Y’s. (A) correlation (B) covariance (C) variance (D) standard deviation 7. The X measurements X 1 , … , X n are to be taken on a sample of n individuals from the population. The statistic 2 2 2 X 1 − X  X 2 − X … X n − X S  n−1 is called the sample ____. (A) correlation (B) covariance (C) variance (D) standard deviation 2 1 8. The X measurements X 1 , … , X n are to be taken on a sample of n individuals from the population. The statistic 2 S 2 X 1 − X  X 2 − X … X n − X n−1 2 is called the sample ____. (A) correlation (B) covariance (C) variance (D) standard deviation 9. Researchers measured the percent body fat and the preferred amount of salt (percent weight/volume) for several children. Here are data for seven children. Preferred amount of salt x : Percent body fat y : 0. 2 0. 3 0. 4 0. 5 0. 6 0. 8 1. 1 20 30 22 30 38 23 . 30 The sample mean x of the x values is ___. (A) 0. 5571428571 (B) 27. 57142857 (C) 0. 5 (D) 30 10. (continuation of 9) The sample standard deviation of the y values rounded to nine decimal places is ___. (A) 6. 267831705 (B) 0. 310145895 (C) 0. 682689409 (D) 0. 9973000656 11. (continuation of 9) The sample standard deviation of the y values rounded to nine decimal places is ___. (A) 6. 267831705 (B) 0. 310145895 (C) 0, 8 (D) 20 12. (continuation of 9) The sample correlation between percent body fat and preferred amount of salt is ___. (A) 0. 2976278855 (B) 0. 578571 (C) 0 (D) 1 13. The population correlation  is alway between −1 and 1, inclusive. (A) True (B) False (C) Not enough information provided (D) || is always greater than 1. 14. The sample correlation r can be less than −1 or greater than 1. (A) True (B) False (C) not enough information is provided. (D) r is always greater than 1. 15. According to Moore, Notz, and Fligner (2021), a correlation based on averages rather than individuals is called an ___ correlation. (A) ecological (B) average (C) variable (D) right 2 16. The measurements X and Y are to be taken on a sample of individuals in a sample of size n  5. Suppose we obtain the following observations x: 1 2 3 4 5 y : 1 4 9 16 25 . Here is a plot of these data. y 20 10 0 0 1 2 3 4 5 x The sample correlation r for these data is ___. (A) 1 (B) 0. 9811049103 (C) 0. 9625668449 (D) 0 17. The measurements X and Y are to be taken on a sample of individuals in a sample of size n  11. Suppose we obtain the following observations x : −5 −4 −3 −2 −1 0 1 2 3 y : 25 16 9 4 1 4 5 . 0 1 4 9 16 25 The sample correlation r for these data is ___. (A) 1 (B) 0. 9811049103 (C) 0. 9625668449 (D) 0 18. The measurements X and Y are to be taken on a sample of individuals in a sample of size n  11. Suppose we obtain the following observations x : −5 −4 −3 −2 −1 0 1 2 3 4 5 y : −5 −4 −3 −2 −1 0 1 2 3 46 5 . The sample correlation r for these data is ___. (A) 1 (B) 0. 9811049103 (C) 0. 9625668449 (D) 0 3 19. How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs. Brother (x) 71 68 66 67 70 71 70 73 72 65 73 Sister (y) 69 64 65 63 65 62 65 64 66 59 62 . The sample correlation r is ___. (A) 7. 654545455 (B) 2. 5 (C) 0. 3517291299 (D) 6. 6 20. (continuation of 19) The standard deviation of the y measurements is ___. (A) 2. 766685921 (B) 2. 569046516 (C) 6. 6 (D) 7. 654545455 s 21. (continuation of 19) Recall that sample correlation r  s xx,ys y . An expression useful in determining the sample covariance s x,y is ___. rs (A) rs x s y (B) rss yx (C) s xrs y (D) s xy 4