Reverse engineering the confidence interval. The 95% confidence interval in Your textbook exercise, Gerstman Exercise 10.12 (5.7 to 6.5 pounds) was calculated with the usual formulaConfidence intervals constructed in this way overline x pm mathbb Z 1- alpha 2 - sigma sqrt n are symmetrical around the mean;is the mid-point of the confidence interval. Question 9: what is the value of the sample mean used to calculate the confidence interval? Question 10: what is the margin of error of the confidence interval? Question 11: what is the standard error of the estimate? Question 12: calculate a 99% confidence interval for μ? Question 13: the sample mean is significant different from 7.2 pounds at a=0.05. Is the difference significant at a =0.01?
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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Step 1: Obtain the value of the sample mean used to calculate the confidence interval.
VIEWStep 2: Obtain the margin of error of the confidence interval.
VIEWStep 3: Obtain the standard error of the estimate.
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