# true mean

#### roby

##### New Member
Hi can you help me with another question please. i have been given the critical dimension of a random sample of 16 auto crankshafts measured in mm 224.120, 224.001.223.980 etc and it says the true dimension is 224.05 mm. then they ask is there any evidence that the true dim is not 224.05mm. how do i find the true dimension. then i have to state the hypotheses find the observed value?? and make comments based on the P-value. Then it says if the pop sd is 0.8mm what sample size is required for estimating the true mean dimension to within plus or minus 0.2mm with 95%confidence. Help this is my first and only subject for data analysis as a prerequisite for psychology and my text book is of little help to me.
thanks
Roby

#### JohnM

##### TS Contributor
You're given the true dimension --> 224.05. You need to do a nondirectional hypothesis test to see if the sample dimension (mean of the sample) is significantly different from the true dimension.

Ho: mu = 224.05
Ha: mu <> 224.05

Z = (x - mu) / (s / sqrt(n))

x = sample mean
mu = 224.05
s = sample standard deviation
n = sample size

Find the probability of z.

For the sample size portion of the question, we have a post in the Examples section that covers this (Sample Size Determination).