Question

A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a random sample of 15 rings were measured, and the mean and standard deviation of the sample were used to construct a 95 percent confidence interval for the population mean width of the rings.
A) Calculate the 99% two-sided confidence interval on the true mean piston diameter.
B) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.

Answer 1

Answer:

a) 74.0353 < u <  74.0367

b) 74.036 < u

Step-by-step explanation:

Given:

- Sample size n = 15

- Standard deviation s.d = 0.0001 in

- Sample mean x_bar = 74.036

Find:

A) Calculate the 99% two-sided confidence interval on the true mean piston diameter.

Solution:

- For 99% CI, We have a = 0.01 , and Z_a/2 = 2.58

------> (x_bar - Z_a/2*s.d / sqrt(n)) < u <  (x_bar + Z_a/2*s.d / sqrt(n))

------> (74.036 - 2.58*0.0001 / sqrt(15)) < u <  (74.036 + 2.58*0.0001 / sqrt(15))

------>                               74.0353 < u <  74.0367

Find:

B) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.

Solution:

- For 95% lower CI, We have a = 0.05 , and Z_a = 1.645

------> (x_bar - Z_a/2*s.d / sqrt(n)) < u

------> (74.036 - 1.645*0.0001 / sqrt(15)) < u

------>                               74.036 < u