4   2. Marc took a random sample of 16 students from a school and for each student recorded • the number of letters, x, in their last name • the number of letters, y, in their first name His results are shown in the scatter diagram on the next page. (a) Describe the correlation between x and y. (1) Marc suggests that parents with long last names tend to give their children shorter first names. (b) Using the scatter diagram comment on Marc’s suggestion, giving a reason for your answer. (1) The results from Marc’s random sample of 16 observations are given in the table below. x 3 6 8 7 5 3 11 3 4 5 4 9 7 10 6 6 y 7 7 4 4 6 8 5 5 8 4 7 4 5 5 6 3 (c) Use your calculator to find the product moment correlation coefficient between x and y for these data. (1) (d) Test whether or not there is evidence of a negative correlation between the number of letters in the last name and the number of letters in the first name. You should • state your hypotheses clearly • use a 5% level of significance (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________