To calibrate a measuring instrument, the following successive measurements were
ID: 3220946 • Letter: T
Question
To calibrate a measuring instrument, the following successive measurements were made on a rod known to have exact length 35 cm: 36.20, 36.22, 36.25, 36.26, 36.28, 36.30, 36.32, 36.35. Considering this to be a simple random sample (SRS) of the population of measurements on this rod, it possible to estimate the "uncertainty" associated with measurements coming from is this instrument? Explain Considering this to be a simple random sample (SRS) of the population of measurements on this it possible to estimate the bias associated with measurements coming from this rod, is instrument? Explain. Is it reasonable to treat these as a SRS of measurements from the population of measurements coming from this instrument? Explain.Explanation / Answer
1.If by “uncertainty” you mean the random error inherent in the instrument then one can estimate that by calculating sample standard deviation of the sample measurements because it a measure of amount of variation of a set of data values.
2.It is also possible to calculate the bias associated with the instrument by using the estimate of population mean of the measurements. The sample mean of the simple random sample is the estimate for the population mean. The difference between the Estimate of population mean and the true value of the rod length will serve as an estimate of bias.
3.Simple Random Sampling is a method of sampling in which each and every unit of population has an equal chance of selection. As we are measuring the length of the rod using only one instrument; we have only one probability distribution associated with measurements. And a sample from a single probability distribution is always a simple random sample. Therefore we can treat these samples as SRSs.
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