### MS 150 Statistics Quiz 08 Fall 2003 8 to 9 • Name: _______________

#### Hypothesis Testing Using Confidence Intervals

##### Microprocessor Controlled Flow Controller

Mechanical engineer Behnam Amin has developed an "intelligent" liquid flow valve using a miniature embedded microprocessor that harnesses the power of advanced modular electronics to control the flow. The response time of the control valve had a mean of 2.17 seconds with a standard deviation of 0.472 after performing 25 tests on the control valve. These valves are used in applications such as aircraft fuel-tank level control systems.

Construct a 99% confidence interval for the population mean response time.

1. The confidence interval for the population mean response time µ is:
_________ < µ < _________
2. The older analog flow controllers had a mean response time of 3.44 seconds. Consider this as population mean, a historically known value. Using the 99% confidence interval calculated above, determine whether the new microprocessor controlled flow valve is statistically significantly improved over the older analog valve.
Confidence interval statistics
Find a zc value from a confidence level c zc   =ABS(NORMSINV((1-c)/2))
Find a tc value from a confidence level c and sample size n tc   =TINV(1-c,n-1)
Calculate an error tolerance E of a mean for n >= 30 using sx E =zc*sx/SQRT(n)
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. E =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E   x-E<= µ <=x+E