Question 22: The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The population standard deviation is 9. The FDA cannot afford to sample the entire shipment so they take a random sample of 39 bags of flour for evaluation and finds that they contain an average of 78.9 insect parts per 100 grams. Test to see if the entire shipment of wheat is not fit for human consumption. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? H0: insect parts/100 grams H1: insect parts/100 grams Based on the hypotheses, find the following: Test Statistic z = p-value = Based on the above we choose to The correct summary would be: that the entire shipment of wheat is not fit for human consumption. What is the type I error in this situation?

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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Question 22:

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour.

When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The population standard deviation is 9.

The FDA cannot afford to sample the entire shipment so they take a random sample of 39 bags of flour for evaluation and finds that they contain an average of 78.9 insect parts per 100 grams. Test to see if the entire shipment of wheat is not fit for human consumption. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places.

What are the correct hypotheses?

H₀: insect parts/100 grams

H₁: insect parts/100 grams

Based on the hypotheses, find the following:

Test Statistic z =

p-value =

Based on the above we choose to

The correct summary would be: that the entire shipment of wheat is not fit for human consumption.

What is the type I error in this situation?

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food
and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods.
You may be surprised to know that much of the processed food we eat contains insect parts. An example is
flour.
When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number
of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this
number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit
for human consumption. The population standard deviation is 9.
The FDA cannot afford to sample the entire shipment so they take a random sample of 39 bags of flour for
evaluation and finds that they contain an average of 78.9 insect parts per 100 grams. Test to see if the
entire shipment of wheat is not fit for human consumption. Test the claim using a 5% level of
significance. Give answer to at least 4 decimal places.
What are the correct hypotheses?
Ho: Select an answer
?♥
insect parts/100 grams
H₁: Select an answer ?♥
insect parts/100 grams
Based on the hypotheses, find the following:
Test Statistic z =
p-value
Based on the above we choose to [Select an answer
that the entire shipment
The correct summary would be: [Select an answer
of wheat is not fit for human consumption.
What is the type I error in this situation?
Select an answer

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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