Stats Practice Problems

Define a p-value.

The probability of observing your data, or something more extreme, under the null hypothesis

Define Sampling Unit and Observation Unit. Identify the key criterion that these terms. Use full sentences.

The sampling unit is the element that is selected at random. The observation unit is the element that the question is being asked about. The sampling unit is always selected at random, whereas the observation unit does not need to be selected at random

Which of the following statements is FALSE? A. We repeatedly sample a population in practice to create the sampling distribution B. The 'true' sampling distribution does not change among samples C. The population distribution does not change among samples D. The sample mean is variable among different samples E. The estimated standard error is variable among different samples

A

Define a p-value using terminology that is general to all tests.

A p-value is the probability of observing your data (or test score) or something more extreme under the null distribution

Which of the following statements are correct about 95% confidence intervals? A. The interval includes the true population value 5% of the time. B. The width of the interval is different for different samples because of sampling error. C. The interval includes the sample mean 95% of the time. D. Confidence intervals are an alternative way to draw conclusions in Chisquare tests. E. The interval is fixed at +/- 2.

B

Which of the following statements best describes the difference between observational and experimental studies? A. Experimental studies suffer from problems with confounding variables, whereas observational studies can be designed to minimize these. B. Observational studies are correlative, whereas experimental studies are causal. C. Observational studies create problems with interpreting the correct statistical population, while experimental studies do not. D. Observational studies are prospective whereas experimental studies are retrospective. E. The goals for experimental and observational studies are similar; it's just that experimental studies offer more control.

B

(4.1, 11, 8.4, 5.8, 10.2, 19.4, 15.7) Calculate the Inter Quartile Range for the above set of numbers and indicate what range the answer lies within. a) 2 ≤ ANSWER < 4 b) 4 ≤ ANSWER < 6 c) 6 ≤ ANSWER <8 d) 8 ≤ ANSWER < 10 e) 10 ≤ ANSWER < 12

C

Which of the following statements best explains why confidence intervals cannot be used to test for significance in a t-test? A. Confidence intervals do not share a common sampling distribution with ttests. B. Confidence intervals indicate the range over which the true population value lies. C. Confidence intervals are a statement about the sampling distribution of your population, not of the null distribution. D. Confidence intervals do not use the standard error estimated from your sample. E. Confidence intervals are always two-tailed whereas t-test can be one- or twotailed.

C

You have just arrived in Kingston to start your first year, and a group of your friends are exploring the grocery store around the corner from where you live. What graph would best illustrate the change in shopping time (minutes) for each of your friends over the first five times they shop at the store? a) Cumulative histogram b) Boxplot c) Line plot d) None of the answers are correct e) Scatter plot f) Bar graph

C

Consider an observational study that collected data on how long it takes to get help at computer stores. Ten random computer stores were sampled as part of the study and data on both the wait time and average price of a laptop were collected. What graph would be best suited to view the relationship between price and time spent waiting? A. Box plot B. Bar graph C. Pie graph D. Scatter plot E. Histogram

D

In 2003 a group of 300 North Americans with Type 1 diabetes between the ages of 21 and 30 were identified by a medical research group. In 2014 a different group of researchers used both medical histories and questionnaires to quantify key aspects of lifestyle and heart health in their subjects. Which of the following best characterizes the study design? A. Experimental study design B. Stratified survey design C. Case-control survey design D. Cohort survey design E. Simple random survey

D

Iron deficiency is one of the most common nutritional disorders in humans. Your research evaluated how three different diets affect blood iron levels in males and females. Which of the following graphing methods would be most appropriate for this type of data with the goal of highlighting the difference in how males and females responded to diet? A. Scatter plot with distinct symbols representing sex B. Line plot C. Pie chart D. Grouped box plot E. Cumulative histogram

D

STUDY A (used for two questions). Is it better to be a 'morning person' or a 'night person'? While most of us can characterize whether we prefer to stay up late or get up early, this is just a habit, and like any other habit it is something that you can change. You were curious whether people were happier overall with being a morning person (go to sleep early and wake up early) versus a night person (go to sleep late and wakeup late). You decided to test this by inviting 20 random people to spend 1 month as a morning person, and one month as a night person and have them record their happiness level in each month. To make sure differences between months did not influence the outcome, you asked people 10 to go from morning->night and 10 people to go from night-> morning. You then tested whether there was a difference in happiness between being a morning person versus a night person. Identify the most appropriate study design for STUDY A. A. Cohort survey design B. Simple random survey C. Cluster survey design D. Experimental study design E. Case-control survey design

D

Which of the following statements about a p-value is correct? A. It is the probability of observing a Type I error under the null hypothesis. B. It is under the control of the researcher. C. It can be used to decide whether to reject a null hypothesis or not without reference to a threshold. 8 D. It is the probability of observing your test score or something more extreme under the null hypothesis. E. It is used for t-tests and regression, but not for Chi-square tests or ANOVA.

D

Which of the following statements about statistical errors is FALSE? a) The Type I error is set by the researcher. b) The Type I error rate is part of hypothesis testing. c) Type I error is the probability of rejecting the null hypothesis when it is correct. d) The Type I error rate depends on the size of your sample. e) We use the Type I error rate to evaluate whether to reject the null hypothesis.

D

STUDY A (used for two questions). Is it better to be a 'morning person' or a 'night person'? While most of us can characterize whether we prefer to stay up late or get up early, this is just a habit, and like any other habit it is something that you can change. You were curious whether people were happier overall with being a morning person (go to sleep early and wake up early) versus a night person (go to sleep late and wakeup late). You decided to test this by inviting 20 random people to spend 1 month as a morning person, and one month as a night person and have them record their happiness level in each month. To make sure differences between months did not influence the outcome, you asked people 10 to go from morning->night and 10 people to go from night-> morning. You then tested whether there was a difference in happiness between being a morning person versus a night person. Identify the statistical test for STUDY A. A. Single-sample t-test B. Two-sample t-test C. Linear regression D. Chi-square test E. Paired-sample t-test

E

STUDY D (used for two questions). Alongside the growth of YouTube and social media, came a new type of celebrity known as 'influencers'. Influencers have a large number of followers and can sway the popularity of brands and social awareness. As a new psychology graduate student, Meredith was interested in whether these influencers were evenly represented across different types of areas such as travel, gaming or entertainment. Meredith selected 40 random people from a list of the top 1000 social media personalities based on number of followers. For each person, she recorded the area of influence (travel, gaming, entertainment) and whether they even reached the top 20 based on number of followers. For STUDY D, what is the most appropriate statistical test? A. Two-sample t-test B. Confidence intervals C. Paired t-test D. Chi-square test E. One-sample t-test

E

The F-test is used for some of the statistical tests that covered in the course. Explain in words what an observed F-ratio represents using a single-factor ANOVA as an example.

The F-ratio is the ratio of the variation explained by the groups over the unexplained variation

Explain what a null F-distribution represents. Include a clear definition of the F-score (i.e., how is an observed F-score calculated), and then include a clear description of what the null distribution for the F-score represents. Be as specific as possible.

The F-score is the ratio of the variation among categorical groups divided by the residual variation within a group. The null distribution for the F-score represents the variation in that ratio you would expect from repeated sampling of a population where there was no true difference in the means.

A null distribution describes the possible range of outcomes from repeated sampling. Explain in words where this variation comes from.

The variation in a null distribution is caused by sampling error. It is the variation in test scores that would occur if we resampled a population where the null hypothesis is true.

Define a null distribution

the sampling distribution of outcomes for the test statistic under the assumption that the null hypothesis is true

Define sampling error.

the variation among repeated samples that is the result of sampling from a population