A high-end restaurant is considering altering the recipe for its signature sauce, but only if the new recipe is favored by a majority of its customers. The restaurant randomly selected 50 of its customers to participate in a blind taste test where they were asked to taste two unmarked dishes in a random order, one prepared with the old sauce and one prepared with the new sauce, and then to select their favorite. In the 50 taste tests, 27 of the customers preferred the new sauce and 23 of the customers preferred the old sauce. Do these results provide convincing evidence that a majority of the restaurant's customers prefer the new recipe for their signature sauce over the old recipe? Justify your answer.
Added by Maurice J.
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Define the null hypothesis ($H_0$) and the alternative hypothesis ($H_a$): $H_0$: There is no preference between the old and new sauce recipes, i.e., the proportion of customers who prefer the new sauce ($p_{new}$) is equal to the proportion of customers who Show more…
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Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70 judges rated both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the judges tasted Sauce A first, while the other half tasted Sauce B first. Actual results are shown below for “overall liking.” Sauce A Sauce B 6 6 6 2 3 5 7 7 5 7 5 1 3 6 7 5 5 9 6 6 6 7 8 6 4 7 6 8 7 8 5 5 4 5 5 3 7 8 9 6 8 6 5 8 7 7 5 8 6 6 5 6 2 5 7 9 7 2 5 7 6 6 7 7 5 9 7 6 6 8 4 8 7 6 7 7 5 8 6 7 8 9 5 8 5 7 8 7 5 5 8 7 5 7 3 6 8 7 6 5 8 8 5 8 3 8 5 5 5 3 6 7 7 5 1 6 6 8 7 6 7 7 8 6 8 5 7 2 3 8 9 6 6 6 7 8 7 7 5 8 Calculate the mean and standard deviation for each sample. (Round your answers to 3 decimal places.) Sauce A ________ _________ Sauce B _________ __________ Calculate the coefficient of variation for each sample. (Enter your answer as a percentage rounded to 1 decimal place.) CVA % ________ CVB % _________
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Mr. Smith creates a new sauce because he wants to increase his restaurant's sales by creating a burger that reduces gas production. He recruits 100 customers with a history of gas problems. He has 50 of them eat burgers with the new sauce. The other 50 eat burgers with sauce that looks just like the new sauce, but it is really just a mixture of mayonnaise and food coloring. Both groups were told that they were getting the new sauce. Mr. Smith has all of the participants track their production of gas for 24 hours. Mr. Smith finds that customers who ate the new sauce had less gas production for 24 hours. For the study above, what is likely Mr. Smith's hypothesis?
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