Question

Shown in the table are data for the tensile force applied to a steel specimen in thousands of pounds, and y is the resulting elongation in thousands of an inch. construct a 95% confidence interval for B, the elongation per thousand pounds of tensile stress. 1. Determine the least squares estimator Sex Tensile force Elongation 2. Determine the value se? applied (thousandths (thousands of of an inch) 3. The t value for this Cl is: pounds) 4. The lower limit for the Cl is 5. The upper limit for the Cl is - 1 2 14 53 63 76 85

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	1	14	6.2500	1431.3611	94.5833
2	2	33	2.2500	354.6944	28.2500
3	3	40	0.2500	140.0278	5.9167
4	4	63	0.2500	124.6944	5.5833
5	5	76	2.2500	584.0278	36.2500
6	6	85	6.2500	1100.0278	82.9167
Total	21	311	17.5000	3734.8333	253.5000
Mean	3.500	51.833	SSX	SSY	SXY

1)

Sxx

=

'Σ(Xi-X̅)2=

17.5000

2)

error Variance =

s2 =SSE/(n-2)

=

15.6762

3)

for 95 % CI value of t=

2.7760

4)

lower confidence bound=estimated slope-margin of error =

11.858

5)

Upper confidence bound=estimated slope+margin of error=

17.113