stats_ps2_winter24

Stats Problem Set #2 1. In sample #1, data are collected for three couples. X i measures the height of the i th man, and Y i measures the height of the i th man’s girlfriend. The correlation between X and Y is calculated to be exactly -1 . It is _____ that some of the men in sample #1 have girlfriends who are taller than themselves while other men in sample #1 have girlfriends who are shorter than themselves. It is _____ that all three of the men in sample #1 have girlfriends who are shorter than themselves. A) possible, possible B) possible, not possible C) not possible, possible D) not possible, not possible 2. In sample #2, data are collected for three couples. M i measures the height of the i th man, and F i measures the height of the i th man’s girlfriend. The correlation between M and F is calculated to be exactly 1 . It is _____ that some of the men in sample #2 have girlfriends who are taller than themselves while other men in sample #2 have girlfriends who are shorter than themselves. It is _____ that all three of the men in sample #2 have girlfriends who are taller than themselves. A) possible, possible B) possible, not possible C) not possible, possible D) not possible, not possible O ~ v · I

2 3. The covariance between X and Y is calculated and recorded as s XY (and s XY is a positive number). A linear transformation is performed on X . The linearly transformed variable is called W , where W i = (6) X i . The covariance between W and Y is calculated and recorded as s WY . Which statement is correct? A) In this example, s WY would be greater than s XY . B) In this example, s WY would be less than s XY . C) In this example, s WY would be equal to s XY . 4. The covariance between X and Y is calculated and recorded as s XY (and s XY is a negative number). A linear transformation is performed on X . The linearly transformed variable is called W , where W i = 5 + X i . The covariance between W and Y is calculated and recorded as s WY . Which statement is correct? A) In this example, s WY would be less than s XY . B) In this example, s WY would be equal to s XY . C) In this example, s WY would be greater than s XY . 5. The correlation between X and Y is calculated and recorded as r XY (and r XY is positive). A linear transformation is performed on X . The linearly transformed variable is called W , where W i = (-4) X i . The correlation between W and Y is calculated and recorded as r WY . In this example, _____. A) r XY would definitely not be the same as r WY B) r XY might be the same as r WY , but might not be C) r XY would definitely be the same as r WY

4 8. Consider the following sample data: Individual X Y Individual 1 1 0 Individual 2 2 0 Individual 3 3 5 Individual 4 4 0 Individual 5 5 5 What is s XY (rounded to four decimal places)? 9. Consider the following sample data: Individual X Y Individual 1 2 1 Individual 2 4 2 Individual 3 6 9 What is s X (rounded to four decimal places)? 10. In sample #1, data are collected for three couples. X i measures the height of the i th man, and Y i measures the height of the i th man’s girlfriend. The correlation between X and Y is calculated to be exactly 1 . Further, when Y is plotted against X and a line is drawn through the data points, the slope is equal to 1. It is _____ that some of the men in sample #1 have girlfriends who are taller than themselves while other men in sample #1 have girlfriends who are shorter than themselves. It is _____ that all three of the men in sample #1 have girlfriends who are taller than themselves. A) not possible, possible B) not possible, not possible C) possible, possible D) possible, not possible

Section Problems 2 #1) Consider the following sample data: Student Exam #1 ( X ) Exam #2 ( Y ) Student 1 110 58 Student 2 124 72 Student 3 126 83 a) What is s xy ? b) What is s x ? Round your answer to two decimal places. c) What is s y ? Round your answer to two decimal places. d) What is r xy ? Use the standard deviations from above that you rounded to two decimal places. Round your final answer to four decimal places.