In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches.What is the 95 percent confidence interval for the true mean length of the bolt?
A)2.804 to 3.196
B)2.308 to 3.692
C)2.769 to 3.231
D)2.412 to 3.588
E)2.814 to 3.186

Question

Quizplus · Accepted Answer

We will use the formula for confidence interval with sample size less than 30 and unknown population standard deviation:
CI = x̄ ± tα/2 * (s/√n)
where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value for the desired level of confidence (95% in this case) and degrees of freedom (n-1=8).
Using a t-distribution table or calculator, we find t0.025,8 = 2.306.
Substituting the given values we get:
CI = 3 ± 2.306*(0.3/√9) = 3 ± 0.231
Therefore, the 95% confidence interval for the true mean length of the bolt is (3 - 0.231) to (3 + 0.231), which simplifies to 2.769 to 3.231. Hence, the best choice is C.

In a Manufacturing Process a Random Sample of 9 Bolts