A New Weight-Reducing Technique, Consisting of a Liquid Protein Diet

question 6

Essay

A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet. $\begin{array}{l}\text { Person Weight Before Diet Weight After Diet }\\\begin{array}{lll}1 & 165 & 158 \\2 & 210 & 205 \\3 & 203 & 200 \\4 & 212 & 206 \\5 & 219 & 215\end{array}\end{array}$

Summary information is as follows: $\bar { d } = 5 , s _ { d } = 1.58$ .
Test to determine if the diet is effective at reducing weight. Use $\alpha = .10$ .

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Definitions:

Tax Liability

The total amount of tax that an individual or entity is legally obliged to pay to a taxing authority based on their income, assets, or activities.

Taxable Income

The amount of an individual's or a company's income used to determine how much tax they owe to the government in a given year.

Subsidy Benefit

A financial advantage or aid given by the government or another organization to support an entity, reducing its costs.

Marginal Tax Rate

The rate at which the last dollar of income is taxed, indicating the rate of tax that applies to each additional dollar of income.