Question

A chemist measures the haptoglobin concentrations (in grams per liter) in the blood of eight healthy adults. Following are the values: 1.82 ,3.32, 1.07, 0.27, 0.49, 3.79, 0.15, 1.98 Obtain a 95% confidence interval for the mean haptoglobin concentration in adults.

Answer 1

Solution:

x	x2
1.82	3.3124
3.32	11.0224
1.07	1.1449
0.27	0.0729
0.49	0.2401
3.79	14.3641
0.15	0.0225
1.98	3.9204
∑x=12.89	∑x2=34.0997

Mean ˉx=∑xn

=1.82+3.32+1.07+0.27+0.49+3.79+0.15+1.98/8

=12.89/8

=1.6113

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√34.0997-(12.89)28/7

=√34.0997-20.769/7

=√13.3307/7

=√1.9044

=1.38

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,7 =2.365

Margin of error = E = t/2,df * (s /n)

= 2.365 * (1.38 / 8)

= 1.15

Margin of error = 1.15

The 95% confidence interval estimate of the population mean is,

- E < < + E

1.61 - 1.15 < < 1.61 + 1.15

0.46 < < 2.7

(2.70, 3.70 )