Question

1.) The data below were gathered on a random sample of 5 basking sharks, swimming through the water and filter-feeding, i.e. passively letting the water bring food into their mouths.

Mean speeds for basking sharks
Body Length	Mean speed
(meters)	(meters/second)
4.0	0.89
4.5	0.83
4.0	0.76
6.5	0.94
5.5	0.94

a) Construct the equation of the linear regression line. ^y (2 decimal places)

2.) A random sample of 20 death certificates in Hawaii gave the following data about the life span (in years) of Hawaii residents. Assume that lifespan is approximately normally distributed for this population.

72    77    68    69    81    85    93    97    56    75    19    71    78    86    94    47    83    66    84    27

Calculate a POINT ESTIMATE of the population mean of life span in Hawaii

Answer 1

1) Solution:

X	Y	XY	X^2	Y^2
4	0.89	3.56	16	0.7921
4.5	0.83	3.735	20.25	0.6889
4	0.76	3.04	16	0.5776
6.5	0.94	6.11	42.25	0.8836
5.5	0.94	5.17	30.25	0.8836

n	5
sum(XY)	21.62
sum(X)	24.50
sum(Y)	4.36
sum(X^2)	124.75
sum(Y^2)	3.83

= a + bx

= 0.61 + 0.05X

2) Solution:

We have a sample .

Sample Size n = 20

We prepare a table.

	X	X2
	72	5184
	77	5929
	68	4624
	69	4761
	81	6561
	85	7225
	93	8649
	97	9409
	56	3136
	75	5625
	19	361
	71	5041
	78	6084
	86	7396
	94	8836
	47	2209
	83	6889
	66	4356
	84	7056
	27	729
Sum =	1428	110060

Sample Mean =   = 1428/20 = 71.4

Point Estimate of the population Mean = Sample Mean   = 71.4