A student is performing measurements in the chemistry laboratory and recording the results in a lab report. The student performs the experiment four times and records the mean x of the four measurement trials. Suppose that the chemistry teacher has found that ? = 12 milligrams from previous similar experiments.(a) What is the standard deviation of the student's mean result? (That is, if the student kept on making four measurements and averaging them, what would be the standard deviation of all the x values?)mg(b) How many times must the student perform the measurement to reduce the standard deviation of x to 2?n = (c) Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.-The average of several measurements will always be an unbiased estimate of the mean.-The average of several measurements is more likely than a single measurement to be close to the mean.-The result of a single measurement will never be close to the mean.-Taking several measurements reduces the likelihood of reporting error.

Question

A student is performing measurements in the chemistry laboratory and recording the results in a lab report. The student performs the experiment four times and records the mean x of the four measurement trials. Suppose that the chemistry teacher has found that ? = 12 milligrams from previous similar experiments.(a) What is the standard deviation of the student&#039;s mean result? (That is, if the student kept on making four measurements and averaging them, what would be the standard deviation of all the x values?)mg(b) How many times must the student perform the measurement to reduce the standard deviation of x to 2?n = (c) Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.-The average of several measurements will always be an unbiased estimate of the mean.-The average of several measurements is more likely than a single measurement to be close to the mean.-The result of a single measurement will never be close to the mean.-Taking several measurements reduces the likelihood of reporting error.

stadfeste8ru · Accepted Answer

Given Information:The student performs the experiment four times and records the mean x― of the four measurement trials.n=4The teacher has found that Standard deviation σ=12 milligrams from previous similar experiments.(a) To find the standard deviation of the student&#039;s mean result:Standard deviation of sample means is give by the formula:σx―=σn=124=6Thus, the standard deviation of the student&#039;s mean result is 6 milligrams.(b) How many times must the student perform the measurement to reduce the standard deviation of x― to 2:We are asked to find the sample size n:Standard deviation of means x― must be reduced to 2 i.e., σx―=2Using the above formula:σx―=σn2=12nn=122n=6(n)2=(6)2n=36Thus, the required samples size is n = 36 measurements.(c) Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.The average of several measurements is likely to be a better approximation of the true mean than a single measurement.Thus, the correct option is: The average of several measurements is more likely than a single measurement to be close to the mean.

guinder0ir · Accepted Answer

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A student is performing measurements in the chemistry

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