Question

PHY 1362 Pre-Lab Activity: Mechanical Equivalent of Heat Confidence Limits When a scientist reports a final value of a measured quantity this value must be reported with a certain level of confidence. In the statistical theory the stochastic nature of the measurement process. f error there is an exact definition of confidence limits based upon The method of confidence limits is of great value and importance when comparing to a known standard or given quantify these ideas we shall make some simplifying assumptions: value such as the mechanical equivalent of heat. To l. The measured value is found to be-test Ơ 2. The distribution associated with x is Gaussian 3. Therefore the standard deviation of the distribution is ơ pper, mple Which for a large number of measurements reasonable approximations, see Chapter 5 of Taylor. Then the discrepancy, t, is defined to be how far the measured value is from the comparison value measured in multiples of the standard deviation: Xest Xknown e, the number of standard deviations that the measured value differs from the known value. The probability of obtaining an answer that differs from the known by t or more standard deviations is given by the area, in principle found by integration, which is carried out numerically and tabulated in Appendix A of Taylor Although the scientific community will determine whether or not the results are significant it is common to refer to results that are known to be within 5% as alpha significant. In terms of the probability, P, as given by Appendix A-(which is within to) then the probability that the answer is outside this range P(outside to)-1-P(within to) where for a small discrepancy this is a large probability, near 1 (see Chapter $) Questions: . A value for the mechanical equialent of heat is measured to be 4922 + 200 Jkcal. What is the 2. Is this value alpha significant? Notice that the hundredths place in t is given by the top row of the table. discrepancy of this measurement, t? What is the probability that one would obtain a value within one standard deviation of the known, i.e.t 1.0? Therefore what is the probability that it is outside of this range?

Answer 1

Solution for question 1 only.

vert x_best - x_known vert = can be said as total error while measurement which is plusminus 200 So vert x_best - x_known vert = 400 s sigma = 200 s t = vert x_best - x_known vert/sigma = 400 s/200 s t = 2