MATH 120 WEEK 7 EXAM | 2026 QUESTIONS
AND ANSWERS WITH THOROUGH SOLUTIONS
– NEWLY UPDATED SUCCESS GUIDE–AMU.
View answer
1.
Question 1
What is the impact of changing from a 90% confidence interval to a 99% confidence
interval?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: A
Description: A confidence interval represents the range in which we expect the true population
parameter to fall. To be "more confident" (moving from 90% to 99%), you must cast a wider
net. Increasing the confidence level increases the critical value ($z^*$ or $t^*$), which in turn
increases the margin of error and makes the interval wider.
Question 2
What does decreasing the standard deviation of the sample do to the confidence interval?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: B
Description: The standard deviation measures the "noise" or variability in your data. In the
formula for a confidence interval, the margin of error is directly proportional to the standard
deviation (
$$ME = z^* \cdot \frac{\sigma}{\sqrt{n}}$$
, ). If the data is less variable (lower standard deviation), the estimate becomes more precise,
resulting in a narrower (smaller) range.
Question 3
What is the impact of decreasing the sample size?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: A
Description: Sample size ($n$) has an inverse relationship with the width of the confidence
interval. Because $n$ is in the denominator of the standard error formula (
$$\frac{\sigma}{\sqrt{n}}$$
), a smaller sample size results in a larger standard error. Larger errors mean less certainty,
which requires a wider interval to capture the population mean.
Question 4
Which accurately describes widening the range of the confidence interval (by changing the
confidence level)?
A) The range is wider so there is more precision
B) The range is wider so there is less precision
C) The range is wider so the certainty is higher
D) The range is wider so the certainty is lower
Correct Answer: C
Description: There is an inherent trade-off between precision and certainty. A "wider" interval
is technically less precise (it gives you a larger "maybe" pile), but it provides higher certainty
because you are more likely to have actually captured the true mean within that larger range. In
statistics, "certainty" is synonymous with the confidence level percentage.
View answer
5.
A delivery company provides expected time of arrival. The company
wants to provide an accurate suggestion with a 90% confidence level. If
the sample size is 50, the sample average is 35 minutes, the standard
AND ANSWERS WITH THOROUGH SOLUTIONS
– NEWLY UPDATED SUCCESS GUIDE–AMU.
View answer
1.
Question 1
What is the impact of changing from a 90% confidence interval to a 99% confidence
interval?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: A
Description: A confidence interval represents the range in which we expect the true population
parameter to fall. To be "more confident" (moving from 90% to 99%), you must cast a wider
net. Increasing the confidence level increases the critical value ($z^*$ or $t^*$), which in turn
increases the margin of error and makes the interval wider.
Question 2
What does decreasing the standard deviation of the sample do to the confidence interval?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: B
Description: The standard deviation measures the "noise" or variability in your data. In the
formula for a confidence interval, the margin of error is directly proportional to the standard
deviation (
$$ME = z^* \cdot \frac{\sigma}{\sqrt{n}}$$
, ). If the data is less variable (lower standard deviation), the estimate becomes more precise,
resulting in a narrower (smaller) range.
Question 3
What is the impact of decreasing the sample size?
A) The range of values included increases
B) The range of values included decreases
C) The range of values included stays the same
D) It cannot be determined from the information provided
Correct Answer: A
Description: Sample size ($n$) has an inverse relationship with the width of the confidence
interval. Because $n$ is in the denominator of the standard error formula (
$$\frac{\sigma}{\sqrt{n}}$$
), a smaller sample size results in a larger standard error. Larger errors mean less certainty,
which requires a wider interval to capture the population mean.
Question 4
Which accurately describes widening the range of the confidence interval (by changing the
confidence level)?
A) The range is wider so there is more precision
B) The range is wider so there is less precision
C) The range is wider so the certainty is higher
D) The range is wider so the certainty is lower
Correct Answer: C
Description: There is an inherent trade-off between precision and certainty. A "wider" interval
is technically less precise (it gives you a larger "maybe" pile), but it provides higher certainty
because you are more likely to have actually captured the true mean within that larger range. In
statistics, "certainty" is synonymous with the confidence level percentage.
View answer
5.
A delivery company provides expected time of arrival. The company
wants to provide an accurate suggestion with a 90% confidence level. If
the sample size is 50, the sample average is 35 minutes, the standard
