Hypothesis Testing

Question

Suppose a machine produced wooden blocks. The machine is not entirely accurate so the blocks come out with a known standard deviation of 2cm regardless of what length the machine is set to cut. I test 12 blocks and find that they have a sample mean length of 12cm. Find a 90% confidence interval for the true mean length of the blocks the machine creates.

Pick the correct distribution (tcv or zcv) and calculate E and CI

Answer 1

Hi Chad,

Since you know the population standard deviation (2 cm.), you can use a z-confidence interval and zcv:

CI = xbar +/- z* (sigma/sqrt(n))

xbar= sample mean = 12

z* = z-critical value for 90% confidence = 1.645

sigma= pop. standard deviation = 2

n = sample size = 12

CI = 12 +/- (1.645*(2/sqrt(12))

CI = (11.05, 12.95)

Error (E) = z*(sigma/sqrt(n) = 1.645(2/sqrt(12)) = 0.95

You might want to memorize these z-critical values as they come up frequently:

z90% = 1.645

z95% = 1.96

z99% = 2.576

I hope this helps.