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-sliced apples-was packaged to appeal to children. The researchers showed the packaging to a sample of 333 school chldren and asked each whether he or she was wiling to eat the product. Wilingness to eat was measured on a 5-point scale, with 1 -'not willing at all and 5 -"very wilig. The data are summarized as x -3.31 and s -1.97. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) IS -3. Complete parts a and b below. a. Conduct a test to determine whether the true mean wil ness to eat the brand of sliced a les packaged for State the null and alternative hypotheses ildren exceeded 3 se : 005 to make our conclusion. 0- Find the test statistic zRound to two decimal places as needed.) Find the p-value. p-vahue-Round to three decimal places as needed.) p-value = (Round to three decimal places as needed.) What is the appropriate conclusion at = 0.05? OA. Reject Ho There is insufficient evidence to conchude that the true mean response for all school children is greater than 3 OB. Do not reject Ho There is sufficient evidence to conclude that the true mean response for all school children is greater than 3 OC. Reject Ho. There is sufficient evidence to conclude that the true mean response for all school children is greater than 3 OC Reject H. There is sufficient evidence to concude that the true mean response for all school children is greater than 3. OD. Do not reject Ho There is insufficient evidence to conclude that the true mean response for all school children is greater than 3 b. The data (wilingness to eat vahues) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain. A· The sample size is not large enough for the conclusion to be valid. OB. The conchusion is stll valid because the sample size is large enough that the Central Limit Theorem applies. OC Oc. Since the data are not normally distributed, the test statistic is not normally distributed and the conchusion is no longer valid. OD. 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.

Explanation / Answer

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   3  
Ha:    u   =/   3   [ANSWER]

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Getting the test statistic, as              
              
X = sample mean =    3.31          
uo = hypothesized mean =    3          
n = sample size =    333          
s = standard deviation =    1.97          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.871557946   [ANSWER]

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As we can see, this is a    two   tailed test.      
              
Thus, the p value is              
              
p =    0.004084539   [ANSWER]

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As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

Hence,

OPTION C: REJECT HO. THERE IS SUFFICIENT EVIDENCE TO CONCLUDE THAT THE TRUE MEAN RESPONSE FOR ALL SCHOOL CHILDREN IS GREATER THAN 3.

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b)

OPTION B: The conclusion is still valid becasue the sample size is large enough that the central limit theorem applies.

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