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## Quiz 8 : Sampling Distributions

If the sampled population is exactly normally distributed, then the sampling distribution of is also expected to be normal, regardless of the sample size.
Free
True False

True
Explanation: Since the sampled population is normally distributed, the sample size plays no role.

As the sample size increases, the standard deviation of the sampling distribution increases.
Free
True False

False
Explanation: Increasing a sample size will cause the standard deviation of the sampling distribution to decrease (because we are dividing the population standard deviation by n).

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.
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True False

True
Explanation: This distribution of the population of all possible sample means looks, at least roughly, like a normal curve.

The standard deviation of the sampling distribution of the sample mean is σ.
True False
The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.
True False
A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.
True False
The reason sample variance has a divisor of n − 1 rather than n is that it makes the variance an unbiased estimate of the population variance.
True False
If a population is known to be normally distributed, then the single sample mean must equal the population mean.
True False
For any sampled population, the population of all sample means is approximately normally distributed.
True False
A minimum-variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.
True False
If the sampled population distribution is skewed then, in most cases, the sampling distribution of the mean can be approximated by the normal distribution if the sample size, n, is at least 30.
True False
If a population is known to be normally distributed, then the sample standard deviation must equal σ.
True False
The mean of the sampling distribution of is always equal to the mean of the sampled population.
True False
The standard deviation of all possible sample proportions increases as the sample size increases.
True False
If p = .8 and n = 50, then we can conclude that the sampling distribution of is approximately a normal distribution.
True False
If p = .9 and n = 40, then we can conclude that the sampling distribution of is approximately a normal distribution.
True False