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Analyzing Salad Habits: A Statistical Look at 85.5%

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QUESTION:

According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week. A nutritionist suspects that the percentage is higher than this. She conducts a survey of 200 American adults and finds that 171 of them eat salad at least once a week. Conduct the appropriate test that addresses the nutritionist’s suspicions. Use a 0.1 level of significance.

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Analyzing Salad Habits: A Statistical Look at 85.5%
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Examine a survey of 200 adults regarding salad consumption, leading to a sample proportion of 85.5%. Using hypothesis testing and z-test calculations, the video determines whether more than 85% of American adults eat salad weekly. The results offer statistical insights into dietary habits.

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QUESTION:

According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week. A nutritionist suspects that the percentage is higher than this. She conducts a survey of 200 American adults and finds that 171 of them eat salad at least once a week. Conduct the appropriate test that addresses the nutritionist’s suspicions. Use a 0.1 level of significance.

ANSWER:

Step1 of 2:

We have \(\mathrm{n}=200, \mathrm{x}=171, \alpha=0.10\)

\(\hat{p}=\frac{x}{n}=\frac{171}{200}=0.855\)

\(n p_{0}\left(1-p_{0}\right)=25.5>10\)

\(\begin{aligned} 200 * 0.85(1-0.85) & >10 \\ 25.5 & >10 \end{aligned}\)

a). Consider the appropriate null and alternative hypothesis are:

\(\begin{array}{l}H_{0}: p=0.85 \text { against } \\ H_{1}: p>0.85\\ \text{With } \alpha=0.10 \text{ level of significance}\end{array}\)

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