Whenever possible, random selectionshould be used to choose samples in research studies.In random selection, chance determines which individuals are included in the sample. Random selection helps ensure that a sample is representative of the population from which it was chosen. More practically, random selection allows researchers to generalize sample results to some larger population of interest.

(1) Suppose Consumers Union had used random selection to choose a package of Armour Beef Hot Dogs from a single grocery store for testing. If they obtained an average sensory rating for all the hot dogs in the selected package, to what population could they generalize their resultsall Armour Beef Hot Dogs ever produced, all Armour Beef Hot Dogs that have ever been sent to this store, or all Armour Beef Hot Dogs in this store at the time the sample was chosen? Justify your answer.

In this study, Consumers Union recorded several variables for each brand of hot dog, including type of hot dog, protein-to-fat ratio, calories, sodium, and sensory rating. Two of these are quantitative variablescalories and sodium. Type of hot dog, protein-to-fat rating and sensory rating are categorical variables. When we analyze data, the types of graphs and numerical summaries we should use are determined by the type of data we are analyzing. We begin by examining two of the categorical variables: type of hot dog and protein-to-fat rating.

(2) Here is a two-way table that summarizes the protein-to-fat ratings by type of hot dog.

Type of hot dog Beef Meat Poultry Poor 12 12 Below 3 Protein-to-fat avg rating Average 2 6 Above 3 avg Excellent 3Healthy Beef Hot Dogs? 12 10 Count O Poor Below avg Average Protein-to-fat ratingComparing protein-to-fat 12 10 O Beef Count Meat Poor Below avg Average Protein-to-fat ratingComparing prote In-to-fat Comparing protein-to-fat 100%% 100% 90% 90% 80% 70% D Above avg O Poultry D Average Percent Percent Dow arg D Poor 10% 0% Poor Below avg Average Above avg Excelent Bool Poultry Protein-to-ta trating Type of hot dog