A health journal conducted a study to see if packaging a hea

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 388 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 = 3.36 and s = 2.38. Suppose the researchers knew that the mean willingness to cat an actual brand of sliced apples (which is not packaged for children) is mu = 3. Complete parts a and b below. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use alpha = 0.10 to make your conclusion. State the null and alternative hypotheses. Find the test statistic. (Round to two decimal places as needed ) Find the p-value.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   3  
Ha:    u   >   3   [ANSWER, PART A]

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As we can see, this is a    right   tailed test.      
                              
Getting the test statistic, as              
              
X = sample mean =    3.36          
uo = hypothesized mean =    3          
n = sample size =    388          
s = standard deviation =    2.38          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.979486394 [ANSWER, Z STATISTIC]

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Also, the p value is, as this is a one tailed test,              
              
p =    0.00144366   [ANSWER, P VALUE]

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As p < 0.10, we reject the null hypothesis.