,MATH 225N EXAM 2 Statistics | Questions And Answers 2026/2027
Chamberlain
1. A researcher wants to estimate the mean systolic blood pressure of a
population. Which statistic is the best point estimate for the population
mean?
A) Sample proportion
B) Sample mean
C) Sample variance
D) Sample standard deviation
**Correct Answer:** B) Sample mean
**Rationale:** The sample mean (x̄ ) is the best point estimate of the
population mean (μ) because it is unbiased and consistent. The sample
proportion estimates a population proportion, not a mean.
2. A 95% confidence interval for a population mean is calculated as (110,
130). What is the margin of error?
A) 5
B) 10
C) 20
D) 30
**Correct Answer:** B) 10
**Rationale:** The margin of error is half the width of the confidence interval:
(130 − 110) / 2 = 10. The point estimate is the midpoint: 120.
,3. Which of the following will increase the width of a confidence interval for a
population mean?
A) Increasing the sample size
B) Decreasing the confidence level
C) Increasing the confidence level
D) Decreasing the population standard deviation
**Correct Answer:** C) Increasing the confidence level
**Rationale:** A higher confidence level requires a larger critical value (z* or
t*), which widens the interval. Increasing sample size or decreasing standard
deviation narrows the interval.
4. A sample of 100 patients has a mean BMI of 28.5 with a standard
deviation of 4.2. What is the standard error of the mean?
A) 0.042
B) 0.42
C) 4.2
D) 42
**Correct Answer:** B) 0.42
**Rationale:** The standard error of the mean (SEM) is calculated as s / √n =
4.2 / √100 = 4. = 0.42. It measures the variability of the sample mean.
5. A researcher constructs a 99% confidence interval for a population
proportion and obtains (0.45, 0.55). The correct interpretation is:
A) There is a 99% probability that the true population proportion is between
0.45 and 0.55.
, B) We are 99% confident that the true population proportion is between 0.45
and 0.55.
C) 99% of the sample data falls between 0.45 and 0.55.
D) The sample proportion is 0.50 with 99% confidence.
**Correct Answer:** B) We are 99% confident that the true population
proportion is between 0.45 and 0.55.
**Rationale:** Confidence intervals are interpreted in terms of confidence,
not probability. The interval estimates the population parameter, not the
sample data.
6. If the population standard deviation (σ) is unknown, which distribution
should be used to construct a confidence interval for the mean?
A) Standard normal (z) distribution
B) t-distribution
C) Chi-square distribution
D) F-distribution
**Correct Answer:** B) t-distribution
**Rationale:** When σ is unknown, the t-distribution is used with n−1
degrees of freedom. The z-distribution is used only when σ is known or the
sample size is very large.
7. A sample of 25 patients has a mean cholesterol level of 200 mg/dL and a
standard deviation of 20 mg/dL. What is the 95% confidence interval for the
population mean? (t* = 2.064)
A) (191.7, 208.3)
B) (192.0, 208.0)
Chamberlain
1. A researcher wants to estimate the mean systolic blood pressure of a
population. Which statistic is the best point estimate for the population
mean?
A) Sample proportion
B) Sample mean
C) Sample variance
D) Sample standard deviation
**Correct Answer:** B) Sample mean
**Rationale:** The sample mean (x̄ ) is the best point estimate of the
population mean (μ) because it is unbiased and consistent. The sample
proportion estimates a population proportion, not a mean.
2. A 95% confidence interval for a population mean is calculated as (110,
130). What is the margin of error?
A) 5
B) 10
C) 20
D) 30
**Correct Answer:** B) 10
**Rationale:** The margin of error is half the width of the confidence interval:
(130 − 110) / 2 = 10. The point estimate is the midpoint: 120.
,3. Which of the following will increase the width of a confidence interval for a
population mean?
A) Increasing the sample size
B) Decreasing the confidence level
C) Increasing the confidence level
D) Decreasing the population standard deviation
**Correct Answer:** C) Increasing the confidence level
**Rationale:** A higher confidence level requires a larger critical value (z* or
t*), which widens the interval. Increasing sample size or decreasing standard
deviation narrows the interval.
4. A sample of 100 patients has a mean BMI of 28.5 with a standard
deviation of 4.2. What is the standard error of the mean?
A) 0.042
B) 0.42
C) 4.2
D) 42
**Correct Answer:** B) 0.42
**Rationale:** The standard error of the mean (SEM) is calculated as s / √n =
4.2 / √100 = 4. = 0.42. It measures the variability of the sample mean.
5. A researcher constructs a 99% confidence interval for a population
proportion and obtains (0.45, 0.55). The correct interpretation is:
A) There is a 99% probability that the true population proportion is between
0.45 and 0.55.
, B) We are 99% confident that the true population proportion is between 0.45
and 0.55.
C) 99% of the sample data falls between 0.45 and 0.55.
D) The sample proportion is 0.50 with 99% confidence.
**Correct Answer:** B) We are 99% confident that the true population
proportion is between 0.45 and 0.55.
**Rationale:** Confidence intervals are interpreted in terms of confidence,
not probability. The interval estimates the population parameter, not the
sample data.
6. If the population standard deviation (σ) is unknown, which distribution
should be used to construct a confidence interval for the mean?
A) Standard normal (z) distribution
B) t-distribution
C) Chi-square distribution
D) F-distribution
**Correct Answer:** B) t-distribution
**Rationale:** When σ is unknown, the t-distribution is used with n−1
degrees of freedom. The z-distribution is used only when σ is known or the
sample size is very large.
7. A sample of 25 patients has a mean cholesterol level of 200 mg/dL and a
standard deviation of 20 mg/dL. What is the 95% confidence interval for the
population mean? (t* = 2.064)
A) (191.7, 208.3)
B) (192.0, 208.0)
