Answered: Oven thermostats were tested by setting…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Oven thermostats were tested by setting them to 250 °C and measuring the actual temperature of the oven. In a sample of 67 thermostats, the average temperature was 248.2 °C. Assume the population standard deviation is 5.1 °C.

Find the 90% confidence interval for the mean oven temperature in °F, wherein F=1.8C + 32.

What is the confidence level of the interval (475 °F, 480 °F)?

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A 90% confidence interval for the mean temperature is (473 °F, 482 °F). The following statement is True or false? "The probability that the mean temperature is between 473 °F and 482 °F is 90%". Justify your answer

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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