Lecture Notes

ME 322: Instrumentation
Lecture 3
January 27, 2012
Professor Miles Greiner
Normal Distribution
• Population size N
• Sample size n < N
Normal Distribution
• The probability the next sample is within:
Lab 2: Cost Estimates
• What cost is greater than 90% of all current
and future measurements?
Example Problem: based of lab
Assume I measure the Quad and got a cost
estimate of $963 and I know that the
measurement process has led to a cost standard
deviation of $323.
How much money should I add to be 90% sure
that I’ve budgeted enough?
Take n samples of a population (n < N)
Expect: 1) & S from different samples will
be equal.
2) as n increases, expect variation
between samples to be smaller.
Uncertainty un the population mean confidence
Confidence Level
• Confidence Level P
– Probability that the true µ is within the confidence
• How to estimate δ for a given P
If N >30
Confidence Level
If N >30 use student t
Example 6.14 a
We would like to determine the confidence
interval of the mean of a batch of resistors
made using a certain process. Based on 36
readings, the average resistance is 25 Ω and
the sample standard deviation is 0.5 Ω.
Example 6.14 a
Example 6.16
A manufacture of VCR systems would like to
estimate the mean failure time of a VCR brand
with 95% confidence. Six systems are tested to
failure, and the following data )in ours of playing
time) are obtained: 1250, 1320, 1542, 1464, 1275,
and 1383.
If a 95% confidence interval of ± 120 h was found
how many more must be tested to obtain a
confidence interval of ± 50 h.
Example 6.16
Example 6.16
Correlation Coefficient
Correlation Coefficient