1. A business has a large fleet of 500 vehicles. These vehicles have an average
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Question
1. A business has a large fleet of 500 vehicles. These vehicles have an average miles per gallon rating of 21.6 mpg. Although each vehicle’s actual fuel consumption will vary, when the business owner wants to plan how much gasoline he will need for the coming year, he will get an accurate estimate assuming a fleet average of 21.6 mpg. Why?
The fleet average x? is the combination a great number of observations (many vehicles, many miles) so the Law of Large Numbers tells us this average will be very close to the population mean, 21.6.
When using the Central Limit Theorem, we take the mean to be 21.6
The sample mean is unbiased.
Every sample has a mean of 21.6 mpg.
2. Cats live for 14 years on average, with a standard deviation of 2 years. Every five years, a vet takes a simple random sample of 50 cats he had cared for in his practice who had died during the period, and records the mean age at death for each sample. We know the sampling distribution of the sample mean is approximately normal because of
the central limit theorem.
the 68–95–99.7 rule.
the law of large numbers.
the fact that probability is the long-run proportion of times an event occurs
A.The fleet average x? is the combination a great number of observations (many vehicles, many miles) so the Law of Large Numbers tells us this average will be very close to the population mean, 21.6.
B.When using the Central Limit Theorem, we take the mean to be 21.6
C.The sample mean is unbiased.
D.Every sample has a mean of 21.6 mpg.
Explanation / Answer
Ans:
1)Option C is correct.
Consider the random variables X1, X2, ..., Xn as a random sample from a population with mean µ. The average value of these observations is the sample mean. The sample mean is a random variable that is an estimator of the population mean. The expected value of the sample mean is equal to the population mean µ. Therefore, the sample mean is an unbiased estimator of the population mean.
2)Option A is correct.
Sampling distribution of the sample mean is approximately normal because of Central limit theorm
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