Question

Which of the following statements are TRUE?

Note that there may be more than one correct answer; select all that are true.

1. a) All else being equal, the standard deviation of the sampling distribution of the sample mean will be smaller for n = 10 than for n = 40.

b) The value of a statistic does not vary from sample to sample.

c) Statistics have sampling distributions.

d) The value of a parameter does not vary from sample to sample.

e) The sampling distribution of μ is always approximately normal for n > 30.

2. a) The mean and the variance of a continuous uniform random variable are the same.

b) In a continuous uniform distribution, the height of the curve, f(x), is the same for all values of the random variable X

c) For a continuous uniform distribution defined on the interval [a,b], P(X < a) and P(X > b) is undefined.

d) In a continuous uniform distribution, the mean and the median are the same.

e) There are countably infinite values of X in a continuous uniform distribution.

3. a)The standard deviation of the sampling distribution of the sample mean depends on the value of μ.

b) The sampling distribution of the sample mean is approximately normal for large sample sizes, and is sometimes approximately normal for small sample sizes.

c) If we quadruple the sample size, the standard deviation of the sampling distribution of the sample mean would decrease by a factor of 2.

d) We cannot possibly determine any characteristics of a statistic's sampling distribution without repeatedly sampling from the population.

e) If the sampling distribution of the sample mean is approximately normal, then the population from which the samples were drawn must have been normally distributed.

Answer 1

1.

a) All else being equal, the standard deviation of the sampling distribution of the sample mean will be smaller for n = 10 than for n = 40.

The formula for sampling distribution is:

As the sample size increases SE decreases.

hence, given statement is false.

b) The value of a statistic does not vary from sample to sample.

The value of statistic based on sample data. It vary from sample to sample.

hence, given statement is false.

c) Statistics have sampling distributions.

True

d) The value of a parameter does not vary from sample to sample.

True

e) The sampling distribution of μ is always approximately normal for n > 30.

The sampling distribution of sample mean is always approximately normal for n > 30.

hence, given statement is false.

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2. a) The mean and the variance of a continuous uniform random variable are the same.

Not necessary that mean and the variance of a continuous uniform random variable are the same.

hence, given statement is false.

b) In a continuous uniform distribution, the height of the curve, f(x), is the same for all values of the random variable X

True

c) For a continuous uniform distribution defined on the interval [a,b], P(X < a) and P(X > b) is undefined.

True

d) In a continuous uniform distribution, the mean and the median are the same.

True

e) There are countably infinite values of X in a continuous uniform distribution.

True

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3. a)The standard deviation of the sampling distribution of the sample mean depends on the value of μ.

False

b) The sampling distribution of the sample mean is approximately normal for large sample sizes, and is sometimes approximately normal for small sample sizes.

True

c) If we quadruple the sample size, the standard deviation of the sampling distribution of the sample mean would decrease by a factor of 2.

True

d) We cannot possibly determine any characteristics of a statistic's sampling distribution without repeatedly sampling from the population.

False

e) If the sampling distribution of the sample mean is approximately normal, then the population from which the samples were drawn must have been normally distributed.

False