Practice Problems 4

# Practice Problems 4 - Practice Problems 5 1. In a random...

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Practice Problems 5 1. In a random sample of 100 ( HHA ) direct flights from New York to Boston, the average number of passengers was 56.3, with sample standard deviation 11.33. a) Construct a 95% confidence interval for the overall average number of passengers on this route. b) To make a reasonable profit, HHA must average at least 58 passengers per flight on this route. The president of the airline is concerned that the average number of passengers is less than 58. Perform the appropriate test at α = 0.05. c) Suppose the actual overall average number of passengers on this flight is 57. Then in part (b) a ( Type I Error, Type II Error, correct decision ) was made. d) Find the p-value of the test in part (b). e) Using the P-value obtained in part (d), state your decision ( Accept H 0 or Reject H 0 ) for α = 0.10. f) Describe in the context of the problem what happens if Type I Error occurs. g) Describe in the context of the problem what happens if Type II Error occurs. 2. wants to determine the proportion of passengers that bring only carry-on luggage to the flight from New York to Boston. a) In a random sample of 200 passengers, 44 passengers had only carry-on luggage. Is there enough evidence to conclude that more than 20% of all passengers have only carry-on luggage? Use α = 0.10. b) Find the p-value of the test in part (a). c) Find a 90% confidence interval for the overall proportion of passengers who have only carry-on luggage. d) Find the minimum sample size required in order to estimate the proportion of passengers who have only carry-on luggage to within 2% with 90% confidence, if it is known that this proportion is at most 0.30.

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3. In a random sample of 25 direct flights from New York to Boston by Hawk & Hummingbird Airline , the sample mean flight time was 56 minutes and the sample standard deviation was 8 minutes. (Assume the flight times are approximately normally distributed.) a) Construct a 98% confidence interval for the overall mean flight time on this route. b) Test whether the actual overall mean flight time on this route is 1 hour (60 minutes) or it is different at 5% significance level. c) Find the P-value of the test in part (b). d) Using the P-value obtained in part (c), state your decision ( Accept H 0 or Reject H 0 ) for α = 0.01. e) Suppose that the actual overall mean flight time on this route is 58 minutes. Then in part (b) a ( Type I Error, Type II Error, correct decision ) was made. 4. An economist states that 10% of Springfield's labor force is unemployed. A random sample of 400 people in the labor force is obtained, of whom 28 are unemployed. a)
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## Practice Problems 4 - Practice Problems 5 1. In a random...

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