Reading 10: Sampling and Estimation - LOS i, (Part 1) ～ Q following, statements, about, style

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1.Which one of the following statements about the t-distribution is TRUE?

A)   The t-distribution is the appropriate distribution to use when constructing confidence intervals based on large samples.

B)   Compared to the normal distribution, the t-distribution is more peaked with more area under the tails.

C)   The t-distribution approaches the standard normal distribution as the number of degrees of freedom becomes large.

D)   Compared to the normal distribution, the t-distribution is flatter with less area under the tails.

2.Which statement best describes the properties of Student’s t-distribution?

A)   The t-distribution is symmetrical, defined by two parameters and is less peaked than the normal distribution.

B)   The t-distribution is symmetrical, defined by a single parameter and is less peaked than the normal distribution.

C)   The t-distribution is skewed, defined by a single parameter and is more peaked than the normal distribution.

D)   The t-distribution is skewed, defined by a single parameter and is less peaked than the normal distribution.

3.When is the t-distribution the appropriate distribution to use? The t-distribution is the appropriate distribution to use when constructing confidence intervals based on:

A)   small samples from populations with known variance that are at least approximately normal.

B)   large samples from populations with known variance that are nonnormal.

C)   small samples from populations with unknown variance that are at least approximately normal.

D)   large samples from populations with known variance that are at least approximately normal.

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答案和详解如下：

1.Which one of the following statements about the t-distribution is TRUE?

A)   The t-distribution is the appropriate distribution to use when constructing confidence intervals based on large samples.

B)   Compared to the normal distribution, the t-distribution is more peaked with more area under the tails.

C)   The t-distribution approaches the standard normal distribution as the number of degrees of freedom becomes large.

D)   Compared to the normal distribution, the t-distribution is flatter with less area under the tails.

The correct answer was C)

As the number of degrees of freedom grows, the t-distribution approaches the shape of the standard normal distribution. Compared to the normal distribution, the t-distribution is less peaked with more area under the tails. When choosing a distribution, three factors must be considered: sample size, whether population variance is known, and if the distribution is normal.

2.Which statement best describes the properties of Student’s t-distribution?

A)   The t-distribution is symmetrical, defined by two parameters and is less peaked than the normal distribution.

B)   The t-distribution is symmetrical, defined by a single parameter and is less peaked than the normal distribution.

C)   The t-distribution is skewed, defined by a single parameter and is more peaked than the normal distribution.

D)   The t-distribution is skewed, defined by a single parameter and is less peaked than the normal distribution.

The correct answer was B)

The t-distribution is symmetrical like the normal distribution but unlike the normal distribution is defined by a single parameter known as the degrees of freedom and is less peaked than the normal distribution.

3.When is the t-distribution the appropriate distribution to use? The t-distribution is the appropriate distribution to use when constructing confidence intervals based on:

A)   small samples from populations with known variance that are at least approximately normal.

B)   large samples from populations with known variance that are nonnormal.

C)   small samples from populations with unknown variance that are at least approximately normal.

D)   large samples from populations with known variance that are at least approximately normal.

The correct answer was C)

The t-distribution is the appropriate distribution to use when constructing confidence intervals based on small samples from populations with unknown variance that are either normal or approximately normal.