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Test Surveys of Customers for Red Lobster Restaurant

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The Red Lobster Restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% of customers rate the food as being excellent? Develop a 99 percent confidence interval over the value of the population proportion of customers who view the food as being excellent. Can the claim be justified based on this evidence at the 1 percent significance level?

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This solution provides a detailed, step by step calculation of the given statistics problem.

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(a) n = 460

p = 0.75

p' = 0.70

Standard Error, SE = sqrt {p(1 - p)/n} = 0.0214

z = (p' - p)/SE = (0.70 - 0.75)/0.0214 = -2.3364

P(p' < ...

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