ME 322: InstrumentationLecture 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?

Uncertainty

Take n samples of a population (n < N)

Expect: 1) & S from different samples will not be equal.

2) as n increases, expect variation between samples to be smaller.

Uncertainty un the population mean confidence interval.

Confidence Level

• Confidence Level P– Probability that the true µ is within the confidence

interval.

• 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