Question

8) A normally distributed set of population scores has a mean of 65 and a standard deviation of 10.2. The mean, of the sampling distribution of the mean, for samples of size 48 equals _________.

9) For the population and sample size given in question 8, the standard error of the mean equals _________.

Answer 1

The mean of a sampling distribution

For samples of size 48, the mean of the sampling distribution of the mean is 65 and the standard error of the mean is approximately 1.477.

As given, A normally distributed set of population scores has a mean of 65 and a standard deviation of 10.2. Therefore, μ = 65 and σ = 10.2For samples of size n = 48, the mean of the sampling distribution of the mean will be the same as the population mean: μ_M = μ = 65 Hence, the mean of the sampling distribution of the mean is 65.

9) For the population and sample size given in question 8, the standard error of the mean can be calculated using the formula: SEM = σ/√where σ = standard deviation of the population = sample size Substituting the values in the formula, we get: SEM = 10.2/√48 ≈ 1.477Hence, the standard error of the mean is approximately 1.477.

Answer: For samples of size 48, the mean of the sampling distribution of the mean is 65 and the standard error of the mean is approximately 1.477.

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