Pregunta
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. As the size of a sample increases, the mean of the distribution of sample means increases. Choose the correct answer below. A. False. The mean of a distribution of sample means changes independently of the corresponding sample size. C. False. As the size of a sample increases, the mean of the distribution of sample means does not change. D. False. As the size of a sample increases, the mean of the distribution of sample means decreases.
Ask by Bowman Burns. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The mean of the distribution of sample means does not change as the sample size increases.
Solución
The statement is false. The mean of the distribution of sample means, also known as the sampling distribution of the sample mean, does not change as the sample size increases. It remains equal to the population mean regardless of the sample size.
The correct answer is:
C. False. As the size of a sample increases, the mean of the distribution of sample means does not change.
This is because the mean of the sampling distribution is equal to the population mean, and increasing the sample size does not affect this relationship.
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C. False. As the size of a sample increases, the mean of the distribution of sample means does not change. The mean of the distribution of sample means, also known as the expected value of the sample mean, remains constant regardless of sample size, as it will always be equal to the population mean. So a true statement would be: "The mean of a distribution of sample means remains the same as sample size increases."
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