4.- Customers who arrive at a gas station have complained to Profeco that they receive less gasoline than what is marked on the meter. Profeco sends a supervisor to check the pump. At the gas station pump the supervisor makes 10 measurements in 20 l jugs: 20.5, 19.99, 20.0, 20.3, 19.90, 20.05, 19.79, 19.85, 19.95 and 20.15. If it assumes normality in the measurements of 20 l With 95% confidence: a) Construct a confidence interval for the mean gasoline content of the jugs, suppose that at 0.14 l b) Construct a confidence interval for the mean gasoline content of the jugs, if \sigma is not known.
4.- Customers who arrive at a gas station have complained to Profeco that they receive less gasoline than what is marked on the meter. Profeco sends a supervisor to check the pump. At the gas station pump the supervisor makes 10 measurements in 20 l jugs: 20.5, 19.99, 20.0, 20.3, 19.90, 20.05, 19.79, 19.85, 19.95 and 20.15. If it assumes normality in the measurements of 20 l With 95% confidence: a) Construct a confidence interval for the mean gasoline content of the jugs, suppose that at 0.14 l b) Construct a confidence interval for the mean gasoline content of the jugs, if \sigma is not known.
4.- Customers who arrive at a gas station have complained to Profeco that they receive less gasoline than what is marked on the meter. Profeco sends a supervisor to check the pump. At the gas station pump the supervisor makes 10 measurements in 20 l jugs: 20.5, 19.99, 20.0, 20.3, 19.90, 20.05, 19.79, 19.85, 19.95 and 20.15. If it assumes normality in the measurements of 20 l With 95% confidence: a) Construct a confidence interval for the mean gasoline content of the jugs, suppose that at 0.14 l b) Construct a confidence interval for the mean gasoline content of the jugs, if \sigma is not known.
4.- Customers who arrive at a gas station have complained to Profeco that they receive less gasoline than what is marked on the meter. Profeco sends a supervisor to check the pump. At the gas station pump the supervisor makes 10 measurements in 20 l jugs: 20.5, 19.99, 20.0, 20.3, 19.90, 20.05, 19.79, 19.85, 19.95 and 20.15. If it assumes normality in the measurements of 20 l With 95% confidence: a) Construct a confidence interval for the mean gasoline content of the jugs, suppose that at 0.14 l b) Construct a confidence interval for the mean gasoline content of the jugs, if \sigma is not known.
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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