### MS 150 Quiz 09 Statistics Spring 2004 • Name:

A Sanyo 256T washer forms a whirlpool in the wash tub during the wash cyle. The depth of the center of the whirlpool is proportional to the rotation rate of the water. The following data was recorded for four different spin measurements.

Sanyo 256T washer data
Depth of whirlpool/cm
0
6
11
16
1. _________ Determine the sample size n.
2. _________ Calculate the sample mean x.
3. _________ Calculate the sample standard deviation sx.
4. _________ Calculate the sample Coefficient of Variation.
5. _________ Determine the class width. Use 5 bins (classes or intervals)
6. Construct a 90% confidence interval for the population mean µ whirlpool depth in centimeters. Note that n is less than 30. Use the sample mean and sample standard deviation to generate your error tolerance E.
1. Make rough sketch on this paper to set up this problem.
2. __________ What is the value for c?
3. __________ How many degrees of freedom?
4. __________ Find t. (We will soon call this "t-critical" or tc)?
5. The error tolerance E = _______________
6. The 90% confidence interval for µ is ____________ ≤ µ ≤ ____________
Basic Statistics
Statistic or Parameter Symbol Equations Excel
Square root     =SQRT(number)
Sample size n   =COUNT(data)
Sample mean x Sx/n =AVERAGE(data)
Sample standard deviation sx or s   =STDEV(data)
Sample Coefficient of Variation CV 100(sx/x) =100*STDEV(data)/AVERAGE(data)
Statistic or Parameter Symbol Equations Excel
Confidence interval statistics
Degrees of freedom df = n-1 =COUNT(data)-1
Find a zc value from a confidence level c zc   =ABS(NORMSINV((1-c)/2))
Find a tc value from a confidence level c tc   =TINV(1-c,df)
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