Answered: Per the USA Food and Drug…

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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Per the USA Food and Drug Administration, frozen custard must contain 1.4% egg yolk solids and at least 10% milkfat. If the percentage of egg yolk solids is less than 1.4%, then it legally must be called ice cream. A food chemist is hired on a potential suspicion that Culver’s frozen custard does not meet the legal definition across all their locations, so he decides to sample the vanilla custard at 50 different locations across Wisconsin. The sample mean percentage of egg yolk solids is 1.2%, with a sample standard deviation of 0.5%.

(a) Find a 95% confidence interval for the true mean percentage of egg yolk solids for Culver’s vanilla custard. (You should be using the confidence interval for the mean here, not the proportion.) Use the normal distribution.

(b)If we were to setup a hypothesis test for this situation regarding egg yolk solids, what would the null and alternative hypotheses be?

(d) What would be a Type II error in this situation? Put your answer in context.

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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