1.Which of the following would result in a wider confidence interval? A:

A)   higher degree of confidence.

B)   higher alpha level.

C)   higher point estimate.

D)   greater level of significance.

2.Which of the following statements regarding confidence intervals is TRUE?

A)   The higher the alpha level, the wider the confidence interval.

B)   The relationship between the alpha level and the confidence interval cannot be ascertained.

C)   The lower the alpha level, the wider the confidence interval.

D)   The lower the degree of confidence, the wider the confidence interval.

答案和详解如下：

1.Which of the following would result in a wider confidence interval? A:

A)   higher degree of confidence.

B)   higher alpha level.

C)   higher point estimate.

D)   greater level of significance.

The correct answer was A)

A higher degree of confidence (e.g. 99% instead of 95%) would require a higher reliability factor (2.575 instead of 1.96 assuming a normal distribution). A wider confidence interval corresponds to a lower alpha significance level and the point estimate does not affect the width of the confidence interval.

2.Which of the following statements regarding confidence intervals is TRUE?

A)   The higher the alpha level, the wider the confidence interval.

B)   The relationship between the alpha level and the confidence interval cannot be ascertained.

C)   The lower the alpha level, the wider the confidence interval.

D)   The lower the degree of confidence, the wider the confidence interval.

The correct answer was C)

A higher degree of confidence requires a wider confidence interval. The degree of confidence is equal to one minus the alpha level, and so the wider the confidence interval, the higher the degree of confidence and the lower the alpha level. Note that the lower alpha level requires a higher reliability factor which results in the wider confidence interval.