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 365 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=3.38 and s=2.57. 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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
packaged to appeal to children. The researchers showed the packaging to a sample of
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
willing at all" and
willing." The data are summarized as
and
Suppose the researchers knew that the
Complete parts a and b below.
![### Study on the Influence of Packaging on Children's Willingness to Eat Healthy Food
A health journal conducted a study to investigate whether 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 365 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 follows:
- Sample mean (\(\bar{x}\)) = 3.38
- Sample standard deviation (\(s\)) = 2.57
The researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is \(\mu = 3\).
The task involves conducting a statistical test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeds 3. Use \(\alpha = 0.01\) for this test.
#### Part A: Conducting the Test
**State the null and alternative hypotheses:**
- \(H_0\) (Null Hypothesis): The mean willingness to eat the sliced apples is equal to 3 (\(\mu \leq 3\)).
- \(H_a\) (Alternative Hypothesis): The mean willingness to eat the sliced apples is greater than 3 (\(\mu > 3\)).
**Find the test statistic:**
\(z = \) [Input Box: Round to two decimal places as needed]
**Find the p-value:**
p-value = [Input Box: Round to three decimal places as needed]
**Determining the conclusion at \(\alpha = 0.01\):**
**Options:**
- A. Do not reject \(H_0\). There is insufficient evidence to conclude that the true mean response for all school children is greater than 3.
- B. Reject \(H_0\). There is insufficient evidence to conclude that the true mean response for all school children is greater than 3.
- C. Reject \(H_0\). There is sufficient evidence to conclude that the true mean response for all school children is greater than 3.
- D. Do not reject \(H_0\). There is sufficient evidence to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6ce828-7421-4579-a347-7b809a44673d%2F453af45c-bdeb-4b92-99c4-8003c36b365b%2F3fffp6i_processed.png&w=3840&q=75)
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