A health journal conducted a study to see if packaging a healthy food product li
ID: 3442689 • Letter: A
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 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.Explanation / Answer
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.
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