Question

A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows:

8.24, 8.25, 8.20, 8.23, 8.24, 8.21, 8.26, 8.26, 8.20, 8.25, 8.23, 8.23, 8.19, 8.25, 8.24.

You have to find a 95% two-sided confidence interval on mean rod diameter. What is the upper value of the 95% CI of mean rod diameter? Please report your answer to 3 decimal places.

Answer 1

Solution :

Given that,

x	x2
8.24	67.8976
8.25	68.0625
8.2	67.24
8.23	67.7329
8.24	67.8976
8.21	67.4041
8.26	68.2276
8.26	68.2276
8.2	67.24
8.25	68.0625
8.23	67.7329
8.23	67.7329
8.19	67.0761
8.25	68.0625
8.24	67.8976
---	---
∑x=123.48	∑x2=1016.4944

Mean ˉx=∑xn

=8.24+8.25+8.2+8.23+8.24+8.21+8.26+8.26+8.2+8.25+8.23+8.23+8.19+8.25+8.2415

=123.4815

=8.232

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

=√1016.4944-(123.48)21514

=√1016.4944-1016.487414

=√0.00714

=√0.0005

=0.0224

n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,14 =2.145

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

= 2.145 * (0.022 / 15)

=0.012

Margin of error = 0.012

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

- E < < + E

8.232 - 0.012 < < 8.232 + 0.012

8.220 < < 8.244

(2.70, 3.70 )