An engineer plans to compute a confidence interval on the true mean inner diameter of the
bearing used to support the crankshaft of a particular engine. She will do this by measuring the ̄
inner diameters of a random sample of these bearings, compute X and, and then computing ̄
?
the interval X these bearings.
1.645σ /?n, where σ XX
is assumed to be known from past experience with
a) The confidence interval that she is computing has what probability that the true mean diameter will be included?
b) Suppose that the following measurements were recorded, in mm, 30.003, 30.004, 29.998, 30.001, 29.996, 30.002 If σX is known from past experience to be 0.003 what is her confidence interval?
c) If the standard deviation is not known, what now would be her confidence interval?
Transcribed Image Text:X +1.6450x/Vn,
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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