Part B) interpret the 99% confidence level, ( select all that apply) A) 99% of all possible random samples of 12 mushrooms of this type have mean cadmium levels that are between the interval's bounds. B. With 99% confidence, the mean cadmium level of all mushrooms of this type is between the interval's bounds. C. 99% of all mushrooms of this type have cadmium levels that are between the interval's bounds. D.There is a 99%chance that the mean cadmium level of all mushrooms of this type is between the interval's bounds. Some governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm). Researchers measured the cadmium levels in a random sample of a certain type of edible mushroom. Thaccompanying table shows the data obtained by the researchers. Find and interpret a 99% confidence interval for the mean cadmium level of all mushrooms of this type. Assume a population standard deviaticadmium levels in mushrooms of this type of 0.30 ppm. (Note: The sum of the data is 7.14 ppm.)Click here to view the data.Click here to view page 1 of the table of areas under the standard normal curve.Click here to view page 2 of the table of areas under the standard normal curve.Mushroom cadmium levelsThe 99% confidence interval is from ppm to ppm.(Round to three decimal places as needed.)0.290.650.750.230.891.181.000.240.460.320.700.43

Introduction: The confidence interval for the population mean, μ at the 100 (1 – α) % level of confidence when the population standard deviation, σ is known, is as follows: Here, n is the sample size, x̄ is the sample mean, and zα/2 is the critical value of the standard normal distribution.Calculation: The desired confidence level is 99%. Thus, This implies that, The sample size is, n = 12. The formula for the sample mean is, x̄ = Σx / n, where the observations are denoted by x, and the summation is taken over all values of x. Here, Σx = 0.29 + 0.65 + 0.75 + 0.23 + 0.89 + 1.18 + 1.00 + 0.24 + 0.46 + 0.32 + 0.70 + 0.43 = 7.14. Thus, the sample mean is, x̄ = Σx / n = 7.14 / 12 = 0.595. The population standard deviation for the car is, σ = 0.30. Using the above values, the required 99% is calculated as follows: Thus, the 99% confidence interval is from 0.372 ppm to 0.818 ppm. The confidence interval is not a measure of probability or chance. As a result, it cannot be said that 99% of all random samples of size 12 will yield a cadmium level or mean level within the given intervals, or that there is a 99% chance that the mean cadmium level is within the bounds of the interval. Rather, the confidence interval gives a measure of confidence. We can say with 99% confidence that the true mean cadmium level is between the bounds of the obtained interval. Thus, option B is correct.

Answered: Part B) interpret the 99% confidence…

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 B) interpret the 99% confidence level, ( select all that apply)

A) 99% of all possible random samples of 12 mushrooms of this type have mean cadmium levels that are between the interval's bounds.

B. With 99% confidence, the mean cadmium level of all mushrooms of this type is between the interval's bounds.

C. 99% of all mushrooms of this type have cadmium levels that are between the interval's bounds.

There is a 99%chance that the mean cadmium level of all mushrooms of this type is between the interval's bounds.

Some governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm). Researchers measured the cadmium levels in a random sample of a certain type of edible mushroom. Th
accompanying table shows the data obtained by the researchers. Find and interpret a 99% confidence interval for the mean cadmium level of all mushrooms of this type. Assume a population standard deviati
cadmium levels in mushrooms of this type of 0.30 ppm. (Note: The sum of the data is 7.14 ppm.)
Click here to view the data.
Click here to view page 1 of the table of areas under the standard normal curve.
Click here to view page 2 of the table of areas under the standard normal curve.
Mushroom cadmium levels
The 99% confidence interval is from ppm to ppm.
(Round to three decimal places as needed.)
0.29
0.65
0.75
0.23
0.89
1.18
1.00
0.24
0.46
0.32
0.70
0.43

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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