A health journal conducted a study to see if packaging a healthy food product li

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 productlong—sliced apples—was packaged to appeal to children. The researchers showed the packaging to a sample of 335 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 equals="not willing at all" and 5 equals="very willing." The data are summarized as x = 3.34 and s equals = 2.06.

Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is equals = 33.

Complete parts a and b below.

part a) Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use equals=0.01

to make your conclusion. State the null and the alternative hypothesis.

H0 = __ Ha = __

Find the test statistic. z = __ Find the p-value. p-value = __

What is the appropriate conclusion at = 0.01?

A) Do not reject H0. There is insufficient evidence to conlude that the true mean response for all school children is greater than 3.

B) Do not reject H0. There is sufficient evidence to conlcude that the true mean response for all school children is greater than 3.

C) Reject H0. There is sufficient evidence to conclude that the true mean response for all school children is greater than 3.

D) Reject H0. There is insufficient evidence to conclude that the true mean response for all school children is greater than 3.

Part 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.

A) The conlcusion is still valid becuase the sampling distribution of the sample mean is always approximately normal, even if the underlying population distribution is not.

B) The sample size is not large enough for the conclusion to be valid.

C) The conclusion is still valid because the sample size is large enough that the Central Limit Theorem applies.

D) Since the data are not normally distributed, the test statistic is not normally distributed and the conclusion is no longer valid.

Explanation / Answer

a)

One-Sample Z

Test of = 3 vs > 3
The assumed standard deviation = 2.06

N Mean SE Mean 99% Lower Bound Z P
335 3.340 0.113 3.078 3.02 0.001

Ho= =3 Vs Ha= >3

Z = 3.078

p=0.001

Here p-value is less than 0.01 so we Reject Ho

C) Reject H0. There is sufficient evidence to conclude that the true mean response for all school children is greater than 3.

>>>>>>>>

b)

See here sample size is greater than 30 so according Central limit therom sample size is greater than 30 then distribution goes to normal

So the answer is C)

C) The conclusion is still valid because the sample size is large enough that the Central Limit Theorem applies.

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