All random samples of size n = 9 are selected from a normal population with u = 55 and o = 10, and the mean is computed for each sample. Then, all the possible samples of size n = 36 are selected from the same population, and the mean is computed for each sample. Which statement below is true.

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All random samples of size \( n = 9 \) are selected from a normal population with \( \mu = 55 \) and \( \sigma = 10 \), and the mean is computed for each sample. Then, all the possible samples of size \( n = 36 \) are selected from the same population, and the mean is computed for each sample. Which statement below is true?

a. The distribution of sample means for samples of \( n = 9 \) is less variable than the distribution of sample means for \( n = 36 \).

b. The distribution of sample means for \( n = 9 \) has a smaller mean than the distribution of sample means for \( n = 36 \).

c. The distribution of sample means for \( n = 36 \) has a smaller mean than the distribution of sample means for \( n = 9 \).

d. The distribution of sample means for samples of \( n = 36 \) is less variable than the distribution of sample means for \( n = 9 \).
Transcribed Image Text:All random samples of size \( n = 9 \) are selected from a normal population with \( \mu = 55 \) and \( \sigma = 10 \), and the mean is computed for each sample. Then, all the possible samples of size \( n = 36 \) are selected from the same population, and the mean is computed for each sample. Which statement below is true? a. The distribution of sample means for samples of \( n = 9 \) is less variable than the distribution of sample means for \( n = 36 \). b. The distribution of sample means for \( n = 9 \) has a smaller mean than the distribution of sample means for \( n = 36 \). c. The distribution of sample means for \( n = 36 \) has a smaller mean than the distribution of sample means for \( n = 9 \). d. The distribution of sample means for samples of \( n = 36 \) is less variable than the distribution of sample means for \( n = 9 \).
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