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Name: A scale is known to be "low-calibrated" in that it measures an aluminu
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Description: A scale is known to be "low-calibrated" in that it measures an aluminum bar to be 4 grams lower than the actual weight. If ????μold is the mean of all possible measurements of the bar using the old calibration, and ????μnew is the mean of all po

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A scale is known to be "low-calibrated" in that it measures an aluminum bar to be 4 grams lower than the actual weight. If ????μold is the mean of all possible measurements of the bar using the old calibration, and ????μnew is the mean of all possible measurements of the bar using a re-calibrated scale. It is desired that ????−????=4μnew−μold=4.

Consider the test

?0:????−????=4H0:μnew−μold=4 vs. ?0:????−????≠4H0:μnew−μold≠4

Sample after calibration: mean is 95.8 , SD is 4.9 and sample size is 10

Sample before calibration: mean is 89.352 , SD is 4.2 and sample size is 62

We do not know population standard deviations.

What is the p-value? (Hint: best to use software, or else the Desmos Calculator for the 2 sample T and Z test)

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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Sample after calibration: mean is 95.8 , SD is 4.9 and sample size is 10 Sample before calibration: mean is 89.352 , SD is 4.2 and sample size is 62 We do not know population standard deviations. What is the p-value?