Statistics

A car manufacturer is interested in conducting a study to estimate the mean stopping distance for a new type of brakes when used in a car that is traveling at 60 miles per hour. These new brakes will be installed on cars of the same model and the stopping distance will be observed. The cost of each observation is $100. A budget of $12,000 is available to conduct the study and the goal is to carry it out in the most economical way possible. Preliminary studies indicate that s=12 feet for stopping distances.

(a) Are sufficient funds available to estimate the mean stopping distance to within 2 feet of the true mean stopping distance with 95% confidence? Explain your answer.

(b) A regulatory agency requires a 95% level of confidence for an estimate of mean stopping distance that is within 2 feet of the true mean stopping distance. The car manufacturer cannot exceed the budget of $12,000 for the study. Discuss the consequences of these constraints.

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  1. a) there are not sufficient funds. THe required sample size is 139 cars, and if each car will cost $100, then the total cost for estimating the mean stopping distance to within 2 feet of the true mean is $139,000, which is more than the budget will allow.

    b) $12,000 is not enough money to be within 2 feet of the true mean with 95% confidence. $12,000 only allows for 120 cars to be tested, and 139 are required. Given these constraints, the consequences are that the company will not be 95% confident on the mean stopping distance for their brakes, which could lead to car accidents and possible lawsuits.

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