Accepting/Rejecting Measurement of 58mm Using Cahvenenet's Criterion

[stunner5000pt]

Homework Statement

A student makes 10 measurements of length x and gets the results all in mm

46,48,44,38,45,47,58,44,45,43

Using cahuvenenet's criterion should he accept or reject the measurement of 58??

Homework Equations

$\overline{x}$ = average
$sigma_{x}$ = standard deviation
$x_{sus}$ = the measurement we want to reject or accept
$$t_{sus} = \frac{x_{sus}-\overline{x}}{\sigma_{x}}$$
the number of standard deviationsfrom which x sus differes from x bar
n(worse than $x_{sus}$) = N P(outside $t_{sus} \sigma_{x}$)

is n < 0.5 then 58 is rejected

if n > 0.5 then 58 is accepted

The Attempt at a Solution

well the average
x bar = 45.8
standrad deviation = 5.1
$$t_{sus} = 2.4$$ standard deviations

then
P(putside 2.4$\sigma$) = 1 - P(within 2.4 $\sigma$)
= 1 - 0.984
the 0.984 is taken from a table which shows the percent probability
P(within $t\sigma$)= \int_{X-t\sigma}^{X+t\sigma} f_{X,\sigma} (x) dx [/tex], as a function of t

but why is .984?? Why is it that the probability should be chonse to be 0.01 and not 0.00 ... or 0.02??

thanks for your help in advance!

 

[OlderDan]

I'm not sure exactly what you are asking, but the .984 is the probablility that a measurement made on normally distributed data will be within 2.4 standard deviations of the mean. I've never heard of cahuvenenet's criterion, but then I'm hardly an expert in things statistical. .984 is the area under the normal distribution function from -2.4 to +2.4 standard deviations. There are several calculators online for finding and graphing these areas. Here is one of them:

http://www.math.csusb.edu/faculty/stanton/probstat/normal_distribution.html

 

[m2003]

I would first like to clarify that Cahvenenet's criterion is used to determine if a measurement should be accepted or rejected based on statistical analysis, and it is not a definitive answer. It is simply a guideline to help make a decision.

Based on the given measurements, it seems that the measurement of 58mm is an outlier as it is significantly larger than the rest of the measurements. However, before making a decision, it is important to also consider the context of the measurements and the accuracy of the measuring instrument.

If the measurements were taken using a precise and accurate instrument, and there is no reason to suspect any external factors that may have affected the measurement of 58mm, then it is likely that it should be rejected as it deviates significantly from the rest of the measurements.

However, if there is a possibility that the measurement of 58mm could be accurate and there could be external factors that affected the other measurements, then it may be worth further investigation before making a decision.

In summary, while Cahvenenet's criterion can provide guidance, it is important to also consider other factors and use critical thinking when making a decision about accepting or rejecting a measurement.