Name: ______ Mixed Hypothesis Review #3

Name: ______Mixed Hypothesis Review #3

AP Statistics

1) Some automobile dealers are able to sell a new car at a higher price than that advertised by adding extra charges that are often “documentary fees”. In 1990, Illinois became the first state to limit the amount of these extra charges. Suppose a state’s attorney general wants to determine if a difference exists between the mean documentary fees charged by dealers in her state and in a neighboring state. A random sample of 16 dealers in her state charged an average fee of $173.83 with a standard deviation of $55.32, while a random sample of 14 dealers from the neighboring state charged a mean fee of $142.53 with a standard deviation of $34.05. Assuming that charges are normally distributed, is there sufficient evidence to conclude that a difference exists in the mean documentary fee charged by the dealers in the two states?

2) Marine farms must closely monitor temperatures of fishponds since temperature change could result in the death of fish and a large financial loss. To monitor the temperature of a particular pond, 35 readings are taken at the eastern end, and the mean and standard deviation are 72.6 and 0.8 degrees, respectively. For 38 readings at the western end, the mean and standard deviation are 71.9 and 0.4 degrees, respectively. Estimate with 99% confidence the true difference in the mean temperature at the two sites.

3) According to the company, the color distribution of M&M candies is 20% orange, 16% green, 13% red, 14% yellow, 13% brown, and 24% blue. A bag of M&M’s contains 6 orange, 4 green, 9 red, 12 yellow, 5 brown, and 10 blue candies. Does this bag match the color distribution according to the company?

4) As part of its fund-raising program, a civic organization sells an energy-saving light bulb that it claims has an average life of more than 3200 hours. A sample of 8 lights was tested, and their lives in hours appear below. Is there sufficient evidence to support the organization’s claim?

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5) In recent years, applicants for admission to a particular college have had a mean math SAT score of 573. A random sample of 235 applications for next fall’s class had a mean math score of 579 and a standard deviation of 39. Do these results indicate a significant change in the mean math SAT score for this year’s applicants?

6) A manufacturer of lawn mowers has two assembly plants. A random sample of 2000 mowers produced at the first plant revealed that 58 were returned to the dealer for service within 30 days of purchase. For a random sample of 1800 mowers form the second plant, 45 were returned within this time period. Is there sufficient evidence to conclude that the return is greater for the first plant?