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 product long dash —sliced apples long dash —was packaged to appeal to children. The researchers showed the packaging to a sample of 345 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 overbar x equals = 3.46 and s equals = 2.09. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is mu equals = 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

alphaequals=0.01 to make your conclusion.

State the null and alternative hypotheses.

Upper H0: ____

UpperHa: ____

Find the test statistic.

zequals=

(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 alpha equals 0.01?

A.Reject H0. There is sufficient evidence to conclude that the true mean response for all school children is greater than 33.

B.Reject H0. There is tinsufficient evidence to conclude that the true mean response for all school children is greater than 33.

C.Do not reject H0. There is sufficient evidence to conclude that the true mean response for all school children is greater than 33.

D.Do not reject H0. There is insufficient evidence to conclude that the true mean response for all school children is greater than 33.

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

B.Since the data are not normally distributed, the test statistic is not normally distributed and the conclusion is no longer valid.

C.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.

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

Explanation / Answer

Data:     

n = 345    

= 3    

s = 2.09    

x-bar = 3.46    

Hypotheses:     

Ho: 3    

Ha: > 3    

Decision Rule:     

= 0.01    

Degrees of freedom = 345 - 1 = 344   

Critical t- score = 2.337236671    

Reject Ho if t > 2.337236671    

Test Statistic:     

SE = s/Ön = 2.09/345 = 0.112521818   

t = (x-bar - )/SE = (3.46 - 3)/0.112521817530157 = 4.08809607   

p- value = 2.70943E-05    

Decision (in terms of the hypotheses):     

Since 4.08809607 > 2.337236671 we reject Ho and accept Ha

Conclusion (in terms of the problem):     

There is sufficient evidence that > 3

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

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

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