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**Need: The rejection step showing BOTH the p-value
approach (2 points) AND the CV approach (2 points). You do not need
to draw the rejection diagram unless you want to. You must show the
proper p-value and proper CV or CVs, and the rejection rule
(whether in numbers or with the diagram) that led you to your
decision about the null hypothesis. State what happened to the null
and the alternative hypotheses to get full credit.**

**4) Interpret the test result, referencing the alpha
significance level (or percent confidence level), and answering all
questions asked**

**PROBLEM: A hand cream company was
interested in whether customers’ preferences for hand cream are
related to their parental status. On a recent survey of a random
sample of 304 customers, the company asked: "Do you have children
under five years of age that live with you?" The customer answered
“Yes” if they had children under 5 years of age, and “No” if they
did not. The customers were also asked: "What is the most important
characteristic you consider when choosing a hand cream?" The answer
choices were: nice scent; long- lasting; non-greasy; and
all-natural.**

**The company would like you to perform a Test of
Independence to determine if hand cream preference is related to
parental status, at the ? = 0.05 significance level. Is there
evidence that these two variables are related in the population of
customers?**

**The observed frequencies from the sample are given in
the following table:**

2. (14 points) A hand cream company was interested in whether customers' preferences for hand cream are related to their parental status. On a recent survey of a random sample of 304 customers, the company asked: "Do you have children under five years of age that live with you?" The customer answered "Yes" if they had children under 5 years of age, and "No" if they did not. The customers were also asked: "What is the most important characteristic you consider when choosing a hand cream?" The answer choices were: nice scent; longlasting; non-greasy; and all-natural. The company would like you to perform a Test of Independence to determine if hand cream preference is related to parental status, at the \( \alpha=0.05 \) significance level. Is there evidence that these two variables are related in the population of customers? The observed frequencies from the sample are given in the following table: Here is the calculation table for the Chi-Square test statistic: After you calculate and fill out the tables, write the four steps for the hypothesis test on the next page. You need only report the test statistic in Step 2, since the calculation is shown at length above.

Answer: The null hypothesis is not rejected. At a 5% significance level, there is not sufficient evidence to conclude that the hand cream preference and children under 5 at home are dependent; Explanation: The Chi-square test of independence is perfo