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After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage. They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are the conditions for inference met?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the randomness condition is not met.
D. No, the Large Counts Condition is not met.

Answer :

Answer:

A, yes the conditions for inference are met

Step-by-step explanation:

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Final answer:

All conditions for valid inference are met, such as randomness, the 10% condition, and the Large Counts Condition, so the dealership can construct a 99% confidence interval for the proportion of cars with storm damage.

Explanation:

To construct a 99% confidence interval for the true proportion of cars with damage from the storm using the sample data, the car dealership must meet several conditions for valid inference: randomness, 10% condition, and Large Counts Condition.

  • Randomness Condition: The sample must be random. Assuming the dealership randomly selected the cars, this condition is met.
  • 10% Condition: The sample size should not exceed 10% of the population size to avoid the dependency between the trials. Because a car dealership likely has more than 500 cars on the lot (50 being less than 10% of 500), it's reasonable to assume this condition is met.
  • Large Counts Condition: The sample size must be large enough so that both the number of successes (cars with damage) and failures (cars without damage) are expected to be 5 or more. Here, we have 11 damages (successes) and 39 without damage (failures), fulfilling this condition.

Since all the necessary conditions appear to be met, the service department can proceed with constructing the confidence interval.