A researcher investigated whether the temperature of milk, x, can be used to predict the milk's pH content, y. She predicted the pH level of a glass of milk with a temperature of 8.45 degrees to be ŷ= 6.795 a)A 95% confidence interval for the mean pH of all milk with temperature 8.45 degrees is calculated to be (6.76, 6.83). Which of the following is the correct interpretation of this confidence interval? -The mean pH level for all glasses of milk having a temperature of 8.45 degrees is somewhere between 6.76 and 6.83, with 95% confidence. -The pH level for one glass of milk with a temperature of 8.45 degrees is somewhere between 6.76 and 6.83, with 95% confidence. -There is a probability of 0.95 that the mean pH level for this glass of milk with temperature 8.45 degrees is between 6.76 and 6.83. -95% of all glasses of milk with a temperature of 8.45 degrees have a pH level between 6.76 and 6.83. b)Suppose we have a glass of milk whose temperature is 8.45 degrees. We calculate a 95% prediction interval for the pH of this glass of milk to be (6.71, 6.88). Which of the following is the correct interpretation of this prediction interval? Group of answer choices -The mean pH level for all glasses of milk with a temperature of 8.45 degrees is somewhere between 6.71 and 6.88, with 95% confidence. -The pH level for a glass of milk whose temperature is 8.45 degrees is somewhere between 6.71 and 6.88, with 95% confidence. -There is a probability of 0.95 that the mean pH level for all glasses of milk with a temperature of 8.45 degrees is between 6.71 and 6.88. -95% of all glasses of milk with a temperature of 8.45 degrees have a pH level between 6.71 and 6.88.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A researcher investigated whether the temperature of milk, x, can be used to predict the milk's pH content, y. She predicted the pH level of a glass of milk with a temperature of 8.45 degrees to be ŷ= 6.795

a)A 95% confidence interval for the mean pH of all milk with temperature 8.45 degrees is calculated to be (6.76, 6.83). Which of the following is the correct interpretation of this confidence interval?

-The mean pH level for all glasses of milk having a temperature of 8.45 degrees is somewhere between 6.76 and 6.83, with 95% confidence.

-The pH level for one glass of milk with a temperature of 8.45 degrees is somewhere between 6.76 and 6.83, with 95% confidence.

-There is a probability of 0.95 that the mean pH level for this glass of milk with temperature 8.45 degrees is between 6.76 and 6.83.

-95% of all glasses of milk with a temperature of 8.45 degrees have a pH level between 6.76 and 6.83.

b)Suppose we have a glass of milk whose temperature is 8.45 degrees. We calculate a 95% prediction interval for the pH of this glass of milk to be (6.71, 6.88). Which of the following is the correct interpretation of this prediction interval?

Group of answer choices

-The mean pH level for all glasses of milk with a temperature of 8.45 degrees is somewhere between 6.71 and 6.88, with 95% confidence.

-The pH level for a glass of milk whose temperature is 8.45 degrees is somewhere between 6.71 and 6.88, with 95% confidence.

-There is a probability of 0.95 that the mean pH level for all glasses of milk with a temperature of 8.45 degrees is between 6.71 and 6.88.

-95% of all glasses of milk with a temperature of 8.45 degrees have a pH level between 6.71 and 6.88.

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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