Question

Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?

1) For a given sample size, lower confidence means a smaller margin of error. Is the statement true?
A) The statement is true. A larger margin of error creates a wider confidence interval, which is more likely to contain the population parameter.
B) The statement is true. A larger margin of error creates a more narrow confidence interval, which is less likely to contain the population parameter.
C) The statement is false. A larger margin of error creates a more narrow confidence interval, which is less likely to contain the population parameter.
D) The statement is false. A larger margin of error creates a wider confidence interval, which more likely to contain the population parameter.
2) For a specified confidence level, smaller samples provide larger margins of error. Is the statement true?
A) The statement is false. A larger sample size decreases the standard error of the sample proportion, which decreases the margin of error.
B) The statement is true. A smaller sample size increases the standard error of the sample proportion, which decreases the margin of error.
C) The statement is false. A smaller sample size increases the standard error of the sample proportion, which decreases the margin of error.
D) The statement is true. A larger sample size decreases the standard error of the sample proportion, which decreases the margin of error.
3) For a fixed margin of error, smaller samples provide lesser confidence. Is the statement true?
A) The statement is false. A larger sample size increases the standard error of the sample proportion, which, for a fixed margin of error, increases the level of confidence.
B) The statement is false. A smaller sample size increases the standard error of the sample proportion, which, for a fixed margin of error, decreases the critical value, z*
C) The statement is true. A smaller sample size increases the standard error of the sample proportion, which, for a fixed margin of error, decreases the critical value, z*.
D) The statement is true. A larger sample size increases the standard error of the sample proportion, which, for a fixed margin of error, increases the level of confidence.
4) For a given confidence level, halving the margin of error requires a sample half as large. Is the statement true?
A) The statement is false. One can see from the margin of error formula that the margin of error is proportional to n.
B) The statement is true. One can see from the margin of error formula that the margin of error is inversely proportional to the square root of n.
C) The statement is true. One can see from the margin of error formula that the margin of error is proportional to n.
D) The statement is false. One can see from the margin of error formula that the margin of error is inversely proportional to the square root of n.

Answer 1

Explanation:

some are true and some are false

Answer 2

1. A
2. A
3. C
4. B

Explanation:

1) The statement is true. A larger margin of error creates a wider confidence interval, which is more likely to contain the population parameter.

2) The statement is false. A larger sample size decreases the standard error of the sample proportion, which decreases the margin of error.

3) The statement is true. A smaller sample size increases the standard error of the sample proportion, which, for a fixed margin of error, decreases the critical value, z*.

4) The statement is true. One can see from the margin of error formula that the margin of error is inversely proportional to the square root of n.