A health journal conducted a study to see if packaging a healthy food product like junk food would influence children's desire to consume the product. A fictitious brand of a healthy food product-sliced apples-was packaged to appeal to children. The researchers showed the packaging to a sample of 393 school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1="not willing at all" and 5= "very willing." The data are summarized as x= 3.25 and s= 1.94. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is u = 3. Complete parts a and b below. a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use a = 0.05 to make your conclusion. State the null and alternative hypotheses. Họ: Ha: Find the test statistic. z= (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) What is the appropriate conclusion at a = 0.05? O A. Do not reject Hp. There is insufficient evidence to conclude that the true mean response for all school children greater than 3. O B. Do not reject Hp. There is sufficient evidence to conclude that the true mean response for all school children greater than 3. O C. Reject Hg. There is sufficient evidence to conclude that the true mean response for all school children greater than 3. O D. Reject Hg. There is insufficient evidence conclude that the true mean response for all school children greater than 3 b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain. O A. The conclusion is still valid because the sampling distribution of the sample mean is always approximately normal, even if the underlying population distribution is not. O B. The conclusion is still valid because the sample size is large enough that the Central Limit Theorem applies. Oc. The sample size is not large enough for the conclusion to be valid. OD Since the data are nnt normallu dietrihuted the test statistic is not normallv dietrihuted and the conclusion is no Innner valid

A health journal conducted a study to see if packaging a healthy food product like junk food would influence children's desire to consume the product. A fictitious brand of a healthy food product-sliced apples-was packaged to appeal to children. The researchers showed the packaging to a sample of 393 school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1="not willing at all" and 5= "very willing." The data are summarized as x= 3.25 and s= 1.94. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is u = 3. Complete parts a and b below. a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use a = 0.05 to make your conclusion. State the null and alternative hypotheses. Họ: Ha: Find the test statistic. z= (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) What is the appropriate conclusion at a = 0.05? O A. Do not reject Hp. There is insufficient evidence to conclude that the true mean response for all school children greater than 3. O B. Do not reject Hp. There is sufficient evidence to conclude that the true mean response for all school children greater than 3. O C. Reject Hg. There is sufficient evidence to conclude that the true mean response for all school children greater than 3. O D. Reject Hg. There is insufficient evidence conclude that the true mean response for all school children greater than 3 b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain. O A. The conclusion is still valid because the sampling distribution of the sample mean is always approximately normal, even if the underlying population distribution is not. O B. The conclusion is still valid because the sample size is large enough that the Central Limit Theorem applies. Oc. The sample size is not large enough for the conclusion to be valid. OD Since the data are nnt normallu dietrihuted the test statistic is not normallv dietrihuted and the conclusion is no Innner valid

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 health journal conducted a study to see if packaging a healthy food product like junk food would influence children's desire to consume the product. A fictitious brand of a healthy food

product—sliced

apples—was

packaged to appeal to children. The researchers showed the packaging to a sample of

393

school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with

1="not

willing at all" and

5="very

willing." The data are summarized as

x=3.25

and

s=1.94.

Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is

μ=3.

Complete parts a and b below.

Transcribed Image Text:A health journal conducted a study to see if packaging a healthy food product like junk food would influence children's desire to consume the product. A fictitious brand of a healthy food product-sliced apples-was packaged to appeal to children. The researchers showed the packaging to a sample of 393 school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1= "not willing at all" and 5 = "very willing." The data are summarized as x= 3.25 and s = 1.94. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is µ = 3. Complete parts a and b below. a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use a = (0.05 to make your conclusion. State the null and alternative hypotheses. Ho: На Find the test statistic. Z = (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) What is the appropriate conclusion at a = 0.05? A. Do not reject Ho. There is insufficient evidence to conclude that the true mean response for all school children is greater than 3. B. Do not reject Ho. There is sufficient evidence to conclude that the true mean response for all school children is greater than 3. O C. Reject Ho. There is sufficient evidence to conclude that the true mean response for all school children is greater than 3. D. Reject Ho: There is insufficient evidence to conclude that the true mean response for all school children is greater than 3. b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain. O A. The conclusion is still valid because the sampling distribution of the sample mean is always approximately normal, even if the underlying population distribution is not. B. The conclusion is still valid because the sample size is large enough that the Central Limit Theorem applies. C. The sample size is not large enough for the conclusion to be valid. D Since the data are not normally distributed the test statistic is not normally distributed and the conclusion is no longer valid.

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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