Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 0.56 part per million (ppm). A research team measured the cadmium levels in a random sample of edible mushrooms, where the hypothesis test is to decide whether the mean cadmium level in the sample is greater than the governments' safety limit. The null and alternative hypotheses are H0: μ=0.56 ppm, Ha: μ>0.56 ppm. Complete parts (a) through (e) below. d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms equals the safety limit of 0.56 ppm. Choose the correct answer below. A. type I error B. correct decision because a true null hypothesis is not rejected C. correct decision because a false null hypothesis is rejected D. type II error Part 5 e. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms exceeds the safety limit of 0.56 ppm. Choose the correct answer below. A. type I error B. correct decision because a true null hypothesis is not rejected C. type II error D. correct decision because a false null hypothesis is rejected

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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Part 5

e. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean cadmium level in that type of mushrooms exceeds the safety limit of 0.56 ppm.

Choose the correct answer below.

type I error

correct decision because a true null hypothesis is not rejected

type II error

correct decision because a false null hypothesis is rejected

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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