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Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents

A. the bias, if any, which is present in the sampling method.
B. the true population average commute distance.
C. a simple random sample.
D. the sampling distribution of the sample mean.

User Dave Reid
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Final answer:

Option D). A histogram of sample means from repeated random surveys represents the sampling distribution of the sample mean, which, due to the central limit theorem, will approximate a normal distribution as the sample size grows.

Step-by-step explanation:

The question requires you to define the sample mean histogram that is computed from repeated surveys. A histogram of these sample means will show the sampling distribution of the sample mean if you interview ten randomly chosen employees numerous times and calculate the sample mean travel distance for each survey. The central limit theorem, which states that, for a big enough sample size, the distribution of sample means will be about normal regardless of the population distribution, is the foundation for this idea. The true population mean will be the same as the sampling distribution's mean, and the population's standard deviation and sample size will determine the distribution's spread, or standard error.

The reason why the sample mean histogram resembles a normal distribution is largely explained by the Central Limit Theorem. It highlights the significance of sample size and enables statisticians to infer probabilistic conclusions about the distribution of the true population mean from the sample mean. It's also critical to understand that this illustrates the variability of the sample mean around the population mean rather than measuring the sampling method's bias or the genuine population average directly.

User AnKing
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