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.

Question

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.

Accepted Answer

From the given information we conduct Z test for one mean.