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.

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

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

what is all that apply?