Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). Data are collected on a respondent’s age and his/her perception of well-being on a scale from 0 to 100; the data is presented below. Age Happiness
49 62
51 66
41 67
65 71
84 87
41 60
83 86
18 78
36 59
61 63
15 77
86 90
73 70
32 62
84 93
23 72
52 58
72 73
63 63
30 66
72 78
47 60
88 95
69 72

Required:
a. Calculate the sample correlation coefficient between age and happiness.
b. Interpret the sample correlation coefficient between age and happiness.
c. Draw a scatterplot to evaluate your interpretation of the calculated sample correlation value.

a) 0.572

b) There is moderate positive relationship between  age and happiness.

c)

Scatter plot is attached

Step-by-step explanation:

a)

Age(x)  Happiness(y)          x²         y²        xy

49    62            240138443038

51    66            260143563366

41      67            1681        44892747

65    71              422550414615

84    87            705675697308

41      60            1681  36002460

83    86            688973967138

18    78            324  60841404

36    59            129634812124

61    63            372139693843

15    77            225  59291155

86    90            739681007740

73    70            532949005110

32    62                102438441984

84    93              705686497812

23    72            529  51841656

52    58            270433643016

72    73            518453295256

63    63            396939693969

30    66            900  43561980

72    78            518460845616

47    60            220936002820

88    95              774490258360

69    72                  476151844968

sumx=1335

sumy=1728

sumx²=86089

sumy²=127346

sumxy=99485

n=24

Sample correlation coefficient=0.572

b)

Sample correlation coefficient=0.572 shows the moderate positive correlation between age and happiness. As the age increases happiness also moderately increases.

c)

The attached scatter plot shows that the as age increases happiness also moderately increases.

b, i believe, but not sure.

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %