Q: Suppose the IQR for a dataset is 12. According to the standard definition, which value would be considered an outlier?

A value less than $$Q_1 - 1.5$$ \times 12$$

Q: How do you calculate the standard error of the mean?

$$\text{Standard error} = \frac{\sigma}{\sqrt{n}}$$

Question 1

Which of the following best describes the difference between a population parameter and a sample statistic?

Accepted Answer

A population parameter is a fixed value that describes a characteristic of the entire population, while a sample statistic is a value calculated from a subset of the population.

Question 2

A researcher collects data on the number of books read by students in a month. Which type of data is this?

Accepted Answer

Discrete

Question 3

Which plot is most appropriate for displaying the distribution of a continuous variable such as height (in cm)?

Accepted Answer

Histogram

Question 4

If a distribution is right-skewed, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 5

Which measure of spread is more robust to outliers: standard deviation or interquartile range (IQR)?

Accepted Answer

Interquartile range (IQR)

Question 6

Suppose the IQR for a dataset is 12. According to the standard definition, which value would be considered an outlier?

Accepted Answer

A value less than $$Q_1 - 1.5$$ 	imes 12$$

Question 7

Why is the standard deviation of the sampling distribution of the mean smaller than the population standard deviation?

Accepted Answer

Because the sampling distribution averages out the variability, reducing the standard deviation by a factor of $$\sqrt{n}.$$

Question 8

Which of the following is a condition for the Central Limit Theorem to apply?

Accepted Answer

The sample size must be at least 30, or the population distribution must be normal.

Question 9

A researcher wants to test if the average commute time in a city is different from 30 minutes. What is the correct null hypothesis ($$H_0) in $$proper notation?

Accepted Answer

$$H_0$$: \mu = 30$$

Question 10

How do you calculate the standard error of the mean?

Accepted Answer

$$	ext{Standard error} = \frac{\sigma}{\sqrt{n}}$$

Question 11

A 95% confidence interval for the mean is calculated as $$\bar{x} \pm z^* 	imes 	ext{SE}. $$What does the value $$z^*$$ represent?

Accepted Answer

The critical value from the standard normal distribution

Question 12

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we took many samples, about 95% of the calculated intervals would contain the true population mean.

Question 13

Which of the following would reduce the margin of error for a confidence interval, assuming all other factors are held constant?

Accepted Answer

Increasing the sample size

Question 14

In hypothesis testing, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true

Question 15

Which of the following best describes the concept of statistical power?

Accepted Answer

The probability of correctly rejecting a false null hypothesis

Question 16

A researcher performs 20 independent hypothesis tests at $$\alpha = 0.05. $$What is a potential problem with this approach?

Accepted Answer

The probability of making at least one Type I error increases with multiple comparisons.

Question 17

Which of the following statistics is NOT affected by outliers?

Accepted Answer

Median

Question 18

Which of the following has a sampling distribution?

Accepted Answer

The sample mean

Question 19

Suppose you want to estimate the mean systolic blood pressure in a population with a margin of error no greater than 2 mmHg at 95% confidence. Which formula would you use to determine the minimum required sample size $$n$$?

Accepted Answer

$$n = \left( \frac{z^* \sigma}{E} \$$right)^2$$

Question 20

Which plot would be most appropriate to display the sampling distribution of the sample mean from repeated samples?

Accepted Answer

Histogram

ST231W26 Midterm 2 Study Guide: Plots, Sampling Distributions, Hypothesis Testing, and Confidence Intervals

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