Hypotheses for the study of electrical conductivity

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Reference no: EM131137176

Measuring conductivity. State the null and alternative hypotheses for the study of electrical conductivity described in Exercise 15.2. (Is the alternative hypothesis one-sided or two-sided?)

Exercise 15.2:

Measuring conductivity. The National Institute of Standards and Technology (NIST) supplies a "standard iron rod" whose electrical conductivity is supposed to be exactly 10.1. Is there reason to think that the true conductivity is not 10.1? To find out, NIST measures the conductivity of one rod 6 times. Repeated measurements of the same thing vary, which is why NIST makes 6 measurements. These measurements are an SRS from the population of all possible measurements. This population has a Normal distribution with mean µ equal to the true conductivity and standard deviation s= 0.1.

(a) We seek evidence against the claim that s=10.1. What is the sampling distribution of the mean in many samples of 6 measurements of one rod if the claim is true? Make a sketch of the Normal curve for this distribution. (Draw a Normal curve, then mark on the axis the values of the mean and 1, 2, and 3 standard deviations on either side of the mean.)

(b) Suppose that the sample mean is =10.09. Mark this value on the axis of your sketch. Another rod has =9.95 for 6 measurements. Mark this value on the axis as well. Explain in simple language why one result is good evidence that the true conductivity differs from 10.1 and why the other result gives no reason to doubt that 10.1 is correct.

Reference no: EM131137176

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