Question

Ten measurements of impact energy (J) on specimens of A238 steel cut at 60℃ are as follows: 64.1, 64.7, 64.5, 64.6, 64.5, 64.3, 64.6, 64.8, 64.2, and 65.0. Assume that impact energy is normally distributed with ? = 2 J. Find a 95% confidence interval for ?, the mean impact energy.

Using the information from above that impact energy is normally distributed with ? = 2 J, determine how many specimens must be tested to ensure that the 95% confidence interval on ? for A238 steel cut at 60℃ has a width of at most 1 J.

Answer 1

Given:

Sample mean = = 64.53

= 2 J

Critical value:

Z/2 = Z0.05/2 = 1.96          ...................Using standard Normal table

95% Confidence Interval:

Find: Sample size (n)

Where,

= 2 J

E = 1 J

Therefore,