Principles of Statistics
You’ve wrapped up the study guide and are ready for the practice test! Complete the 10 question practice below and check your answers. It’s just practice, so any incorrect answers will help you focus additional study time on those topics.
WarningPlease do keep in mind that we can’t guarantee the accuracy of this quiz, so we do recommend you also run through a full-length practice exam. We’ll recommend some good options in the resources section at the bottom of this page.
Question 1: A(n) ______ is considered the highest level of measurement because it has the characteristics of the other three as well as a meaningful absolute zero.
Nominal is the lowest level as its value is only a label with no ordering implied. Ordinal is one step higher because its values can be ranked. Interval is the next step higher because the intervals between values have meaning. A ratio has all these attributes plus a defined scale that makes zero a meaningful value.
Question 2: Professor Jones’ statistics class of 12 students took an exam, earning the grades in the list below. Prior to the test, the professor claimed that any student with a score two standard deviations or more below the mean score for the class could take the exam again. How many students took the exam a second time?
80, 90, 98, 90, 95, 85, 98, 67, 100, 60, 90, 75
The mean of the exam scores is 86 and the standard deviation of the scores is 13. Thus, two standard deviations equal 26 and a student would need a 60 or below to take the exam again.
Question 3: In Professor Jones’ statistics class, there are equal numbers of women and men taking the class. If a student was selected at random, what is the probability that the student would be a woman with an A on the exam? (referencing the scores listed in question 2)
The probability that a student selected at random would be a woman is 6/12 (6 women/12 total students) or 0.50. The probability that a student selected at random scored an A on the exam is 7/12 (7 scores of 90 or more/12 students) or 0.58. Using the multiplication rule, the combined probability of both events is 0.50*0.58 = 0.29.
Question 4: The probability distribution of a random variable describes the possible values of that variable and how probabilities are assigned to those values. If the random variable is continuous, a ______ describes its probability distribution.
a) Probability histogram
b) Density curve
c) Uniform distribution
d) Normal distribution
Since a continuous random variable can take all values among some group of intervals, the probability any event can be described as the area below a density curve. A probability histogram describes a discrete random variable. Answer choices C. and D. represent types of distributions that can be depicted by a density curve.
Question 5: The correlation between two variables x and y is -0.80. What can be interpreted from this correlation coefficient about the strength and direction of the relationship between x and y?
a) Strong relationship; when x increases, y increases
b) Strong relationship; when x increases, y decreases
c) Weak relationship; when x increases, y increases
d) Weak relationship; when x increases, y decreases
With an absolute value between 0.5 and 1, the relationship between x and y is relatively strong. The negative sign on the correlation coefficient reflects an inverse or negative relationship between x and y, such that the variables rise and fall opposite of one another.
Question 6: Which of the conditions below would allow for rejection of the null hypothesis?
a) The P-value is small
b) The P-value is large
c) The P-value is smaller than the significance level
d) Both A. and C.
A smaller P-value reflects stronger evidence against the null hypothesis. In addition, if the P-value is less than or equal to the significance level, the null hypothesis can be rejected.
Question 7: Referring back to scores on Professor Jones’ exam (question 2), what is the z-score for the grade closest to the mean of the sample?
A z-score is a standardized value of observations in a sample that reflects the number of standard deviations away from the mean for each observation. The z-score will be positive for observations higher than the sample mean and negative for observations below the mean. It is calculated as (observation – mean)/standard deviation. The exam score sample mean is 86 and the closest score to the mean is 85, for a z-score of (85-86)/13 = -0.05.
Question 8: A 95% confidence interval describes ______.
a) A range that includes 95% of the values in the sample.
b) A range that includes 95% of the values of the population.
c) A range that is 95% certain to contain the mean of the sample.
d) A range that is 95% certain to contain the mean of the population.
A confidence interval is an estimate of an unknown, such as the mean of the full population, with an indication of accuracy of the estimate. A 95% confidence interval reflects that the estimate is correct 95% of the time and incorrect 5% of the time.
Question 9: To explore statistical inference among more than two populations, the analysis of variance (ANOVA) methodology must be used. Which of the following is NOT true of one-way ANOVA?
a) The null hypothesis is that the populations means are all equal.
b) The populations are classified in two categories.
c) The total variation is observed in the data as both the variation among group means and variation within groups.
d) The populations are assumed to be normal.
One-way ANOVA is used to analyze more than two populations when there is only one way to classify these populations. To analyze more than two populations when there are two ways to classify the populations, two-way ANOVA is used.
Question 10: Statistical inference through confidence intervals and significance testing can provide confidence in research conclusions. Which question is NOT answered by these tools?
a) Is the sample biased?
b) Is the null hypothesis accepted?
c) Is the observed statistical relationship due to chance?
d) Both A. and B.
Inferential statistics can only support or reject that a relationship exists in the data. If an alternative hypothesis is accepted, then the relationship is not due to chance. If the null hypothesis cannot be rejected, then it does not necessarily mean it can be accepted. The null hypothesis could still be rejected with a new sample, changes to the research design, or by testing a different alternative hypothesis.
More DSST Study Resources
Are you at the beginning of your study process, or just looking for a couple more practice questions to finish prepping for your exam? In either case, you can find some of my favorite resources below. Some of the links below are affiliate (Amazon for instance), which means they’ll pay us a few bucks for every purchase through the link. Feel free to use those links if you want to support the site, but you can also just Google the title or pick the book up at your local library.
Official DSST Practice Test: Ok, so the DSST website isn’t the most inviting, but it will give you the best approximation of the real exam experience. Also, the official practice test is quite affordable (currently just $5 per practice exam).
Mometrix – DSST Principles of Statistics: Textbooks are great as far as they go, but I’d generally recommend you opt for this exam guide instead. It tends to cut through the confusion and help you accelerate your learning process.
InstantCert Academy: Another website with a very dated design, but as ancient as it looks, this is actually an incredibly valuable resource. Basically, you get a massive set of flashcards that you can use to learn Statistics and to really solidify that knowledge so you’re ready for the exam.
Plenty of other resources exist – just do a quick internet search – but these are a fantastic start, and probably all you really need. I’ve personally done some exams with just InstantCert and the official practice test.