3. The National Institute of Standards and Technology (NIST) supplies a “standar
ID: 3151685 • Letter: 3
Question
3. 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 six times. Repeated measurements of the same thing vary, which is why NIST makes six measurements. These measurements are an SRS from the population of all possible measurements. This population has a Normal distribution with mean equal to the true conductivity and standard deviation = 0.1. (a) State the null and alternate hypothesis (b) One set of measurements has mean conductivity = 10.09. What is the test statistic? What is the P-value? Is this outcome statistically significant at the = 0.05 level? At the = 0.01 level? (c) Another set of measurements has = 9.95. Find the test statistic and the P-value
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u = 10.1
Ha: u =/ 10.1 [ANSWER]
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b)
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 10.09
uo = hypothesized mean = 10.1
n = sample size = 6
s = standard deviation = 0.1
Thus, z = (X - uo) * sqrt(n) / s = -0.244948974 [ANSWER, TEST STATISTIC]
Also, the p value is, as this is two tailed,
p = 0.806495941 [ANSWER, P VALUE]
As P > 0.05, IT IS NOT SIGNIFICANT at 0.05 level. [ANSWER]
As P > 0.01, IT IS NOT SIGNIFICANT at 0.01 level. [ANSWER]
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c)
Getting the test statistic, as
X = sample mean = 9.95
uo = hypothesized mean = 10.1
n = sample size = 6
s = standard deviation = 0.1
Thus, z = (X - uo) * sqrt(n) / s = -3.674234614 [ANSWER, TEST STATISTIC]
Also, the p value is
p = 0.000238563 [ANSWER, P VALUE]
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