Washing clothes A consumer group wants to test theeffectiveness of a new “organic” laundry detergent and make recommendations to customers about how to bestuse the product. They intentionally get grass stains on 30white T-shirts in order to see how well the detergent willclean them. They want to try the detergent in cold waterand in hot water on both the “regular” and “delicates” wash cycles. Design an appropriate experiment, indicat-ing the number of factors, levels, and treatments. Explain the role of randomization in your experiment.

Subpart b

Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4025543 64323113 466378156 Column Total 500 500 1000 Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)   (d) P(N and…

In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common. A company that performs this service has developed four different methods of irradiating food. To determine which is best, it conducts an experiment where different foods are irradiated and the bacteria count is measured. As part of the experiment the following foods are irradiated: meat, poultry, veal, tuna, and yogurt. The results are shown below. True or False: It can be inferred at the 5% significance level that at least two of the treatments differ.

A restaurant chain specializing in ice cream deserts contacted you to characterize the market for new franchise locations in Upstate NY. The firm is located in the Southwestern US, and has excellent experience there. However, they are opening a few test locations in Buffalo, Syracuse and Albany in the very near future, and have hired you, an Upstate NY statistical consultant, to collect and analyze the results. These restaurants follow a standard blueprint for design, operation, and location. They run a 2,150 sq foot facility in wealthier suburban areas, and usually locate in new plazas near other specialty restaurants that tend not to compete with them (Starbucks, Panera, Fridays, and similar restaurants.) Existing Southwestern locations take in an average of $82,000 a week in sales, with a highly reliable standard deviation of $5,200. Before deciding on their regional distribution strategy, the firm is opening three test restaurants, one in each city. They want you to examine the…

YOU are in charge of a new products being launched by "Incredible Circuits". Mr. Eleck Trikal, C.E.O. of the company, has seen the need to calculate the Reliability of his new product after 10, 20, 30, and 50 hours of use. This new product is basically made with four components: A B, C, and D; and its design is included below: BAB As a good manufacturing engineer, you take 10 samples for each component, and test them until failure. The following are the times obtained: COMPONENT A: 8, 9, 18, 28, 35+, 43+, 59+, 65, 75, and 78 (+ means censoring) COMPONENT B: 8, 17+, 22, 29, 35, 39, 49+, 55, 59+, and 78 (+ means censoring) COMPONENT C: 2, 23, 24, 35+, 53, 55, 62+, 66+, 76, and 83 (+ means censoring) COMPONENT D: 3, 18, 24, 35, 38, 49, 58, 59, 66, and 79 (no censoring)