Q: A researcher wants to estimate the average systolic blood pressure in a city. She takes a random sample of 100 adults and calculates a sample mean of 130 mmHg with a standard deviation of 20 mmHg. What is the 95% confidence interval for the population mean? (Use $$z^* = 1.96)$$

$$130 \pm 1.96 \times \frac{20}{\sqrt{100}}$$

Question 1

A researcher collects the heights (in cm) of a random sample of adult males from two different cities and displays the results using side-by-side boxplots. What is the primary advantage of using boxplots to compare these two samples?

Accepted Answer

Boxplots display the distribution shape and highlight outliers for each sample.

Question 2

Given the boxplot shown, which of the following statements is most accurate about the data distribution?

Accepted Answer

The data is skewed right and contains possible outliers.

Question 3

Suppose you have a sample of cholesterol levels from a population. The sample mean is $$\bar{x} = 195 mg/dL $$and the sample standard deviation is $$s = 15 mg/dL. $$What is the formula for the standard error of the mean if the sample size is $$n = 25$$?

Accepted Answer

$$SE = \frac{s}{\sqrt{n}}$$

Question 4

A histogram of sample means is shown. What does the shape of this histogram suggest about the sampling distribution as the sample size increases?

Accepted Answer

The sampling distribution becomes more normal.

Question 5

If the population mean is $$\mu = 200$$ and the population standard deviation is $$\sigma = 20$$, what is the expected mean and standard deviation of the sampling distribution of the sample mean for samples of size $$n = 16$$?

Accepted Answer

Mean: $$200$$, Standard deviation: $$5$$

Question 6

Which of the following best describes the Central Limit Theorem?

Accepted Answer

As sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 7

A sample of 36 students has a mean test score of 82 with a standard deviation of 6. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{6}{\sqrt{36}} = 1$$

Question 8

Which scenario best illustrates the law of large numbers?

Accepted Answer

As you flip a fair coin many times, the proportion of heads approaches 0.5.

Question 9

A researcher wants to estimate the average systolic blood pressure in a city. She takes a random sample of 100 adults and calculates a sample mean of 130 mmHg with a standard deviation of 20 mmHg. What is the 95% confidence interval for the population mean? (Use $$z^* = 1.96)$$

Accepted Answer

$$130 \pm 1.96 	imes \frac{20}{\sqrt{100}}$$

Question 10

Which of the following is NOT an assumption for using the Central Limit Theorem for sample means?

Accepted Answer

The population must be normally distributed for any sample size.

Question 11

If a boxplot shows a long whisker on the right side and several points far from the box on the right, what does this indicate about the data?

Accepted Answer

The data is right-skewed with possible outliers.

Question 12

A sample mean is calculated from a sample of size $$n = 49$$ with a sample standard deviation $$s = 14. $$What is the standard error of the mean?

Accepted Answer

$$SE = \frac{14}{\sqrt{49}} = 2$$

Question 13

Which of the following best describes an outlier in a boxplot?

Accepted Answer

A value that is more than 1.5 times the interquartile range above the third quartile or below the first quartile.

Question 14

If the sample size increases, what happens to the standard error of the mean?

Accepted Answer

It decreases.

Question 15

A histogram of sample means from repeated samples of size $$n = 30 is $$approximately normal. What does this suggest about the underlying population distribution?

Accepted Answer

The Central Limit Theorem applies, so the sampling distribution is normal even if the population is not.

Sample Means and Data Visualization in Statistics

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