Question 1

Which of the following best describes the difference between inferential statistics and data mining?

Accepted Answer

Inferential statistics focuses on drawing conclusions about populations from samples, while data mining focuses on finding patterns in large data sets.

Question 2

A researcher collects data on the heights of 1000 students. Which statistical measure would best summarize the center of this data set?

Accepted Answer

The mean

Question 3

Which formula correctly calculates the sample standard deviation $$s$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$}$$

Question 4

Suppose a hospital wants to estimate the average recovery time for a new treatment. They randomly select 50 patients and calculate a 95% confidence interval for the mean recovery time. What does this interval represent?

Accepted Answer

It gives a range of values that is likely to contain the true mean recovery time for all patients, with 95% confidence.

Question 5

Which of the following is a challenge posed by extremely large data sets?

Accepted Answer

Computational limitations can make analysis slow or infeasible.

Question 6

A pharmaceutical company tests whether a new drug lowers blood pressure more than a placebo. Which is the correct null hypothesis for this scenario?

Accepted Answer

$$H_0$$: \mu_{drug} = \mu_{placebo}$$

Question 7

Which of the following best describes a sampling distribution?

Accepted Answer

The probability distribution of a statistic based on all possible samples of a fixed size from a population.

Question 8

A histogram is used to:

Accepted Answer

Display the distribution of a quantitative variable.

Question 9

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is skewed to the right.

Question 10

A researcher wants to test if the average commute time in a city is different from 30 minutes. Which type of hypothesis test should be used?

Accepted Answer

A two-tailed test

Question 11

If a data set contains the values 2, 4, 4, 4, 5, 7, 9, what is the mode?

Accepted Answer

4

Question 12

Which formula is used to calculate a 95% confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 13

Which of the following is an example of a categorical variable?

Accepted Answer

Type of car (sedan, SUV, truck)

Question 14

A student calculates the mean and median of a data set and finds that the mean is much larger than the median. What does this suggest about the data?

Accepted Answer

The data is skewed to the right.

Question 15

Which of the following is the correct formula for the z-score of a value $$x in a $$data set with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 16

A company wants to know if a new training program improves employee productivity. They collect productivity data before and after the program for the same employees. Which statistical test should they use?

Accepted Answer

A paired t-test

Question 17

Which of the following best describes the purpose of exploratory data analysis (EDA)?

Accepted Answer

To summarize the main characteristics of data, often using visual methods.

Question 18

A sample of 100 batteries has a mean lifetime of 500 hours with a standard deviation of 50 hours. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{50}{\sqrt{100}} = 5$$

Question 19

Which of the following is a reason to use statistical software in data analysis?

Accepted Answer

To efficiently perform complex calculations and visualize data.

STAT 145-04: Introduction to Statistics I – Course Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards