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HTH 320 Final Exam: Descriptive and Inferential Statistics, Exams of Statistics

James Madison University (JMU)Statistics

A comprehensive set of questions and answers covering key concepts in descriptive and inferential statistics. it's an excellent resource for students preparing for exams in introductory statistics courses, encompassing topics such as probability, normal distribution, hypothesis testing, and measures of variability. The detailed explanations make it ideal for self-study and exam preparation.

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HTH 320 FINAL EXAM QUESTIONS WITH ACCURATE

SOLUTIONS

1) What is Statistics? -- Answer ✔✔ Branch of mathematics used to summarize,

analyze, and interpret a group of numbers or observations

2) What is inferential statistics? -- Answer ✔✔ Procedures used that allow researches

to infer or generalize observations made with samples to the larger population from

which they were selected.

make decisions

3) What is descriptive statistics? -- Answer ✔✔ Procedures used to summarize,

organize and make sense of a set of scores or observations.

Often presented graphically in tables or as summary statistics

4) Define probability -- Answer ✔✔ the frequency of times an outcome occurs divided

by the total number of possible outcomes

5) What two items do you need to know in order to calculate probability? -- Answer

✔✔ 1. The number of possible outcomes - sample space

2. How often the outcome of interest occurs

Partial preview of the text

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HTH 320 FINAL EXAM QUESTIONS WITH ACCURATE

SOLUTIONS

What is Statistics? -- Answer ✔✔ Branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations
What is inferential statistics? -- Answer ✔✔ Procedures used that allow researches to infer or generalize observations made with samples to the larger population from which they were selected. make decisions
What is descriptive statistics? -- Answer ✔✔ Procedures used to summarize, organize and make sense of a set of scores or observations. Often presented graphically in tables or as summary statistics
Define probability -- Answer ✔✔ the frequency of times an outcome occurs divided by the total number of possible outcomes
What two items do you need to know in order to calculate probability? -- Answer ✔✔ 1. The number of possible outcomes - sample space

How often the outcome of interest occurs

Probability formula -- Answer ✔✔ p(x) = f(x)/sample space
Define normal distribution -- Answer ✔✔ theoretical distribution in which scores are symmetrically distributed above and below the mean, the median, and the mode at the center
List the characteristics of a normal distribution -- Answer ✔✔ 1. Mathematically defined

theoretical
Mean, median, and mode are all located on the 50th percentile
symmetrical
mean can equal any value
SD can equal any positive value
total area under curve is 1 8 tails are asymptotic (approach zero but never touch)

Define z-scores -- Answer ✔✔ value on the x-axis of a standard normal distribution
What is the z-score formula? -- Answer ✔✔ z= x-u/o (population) or z= x-M/SD (sample)
How do you read the unit normal table? -- Answer ✔✔ column A lists z scores column B lists the area between a z score and the mean column C lists the area from a z score toward the tail
Define the Central Limit Theorem -- Answer ✔✔ Regardless of the distribution of scores in a population, the sampling distribution of sample means selected at random

What is a sample? -- Answer ✔✔ Set of individuals, items, or data selected form a population of interest
What is the research method or scientific method? -- Answer ✔✔ Set of systematic techniques used to acquire, modify, and integrate knowledge concerning observable and measurable phenomena
What is an experiment? -- Answer ✔✔ Use of methods and procedures to make observations in which the researcher fully controls the conditions and experiences of participants by applying three requirement elements of control and to isolate cause and effect relationships between variables
What is a non-experiement? -- Answer ✔✔ No treatment A --> O
What is a quasi-experiment? -- Answer ✔✔ A study that lacks randomization but you have a treatment
What is an independent variable? -- Answer ✔✔ The variable that is manipulated in an experiment remains unchanged presumed caused specific conditions of IV are called levels

What is a dependent variable? -- Answer ✔✔ Variable that is measured in each group of a study presumed effect believed to change in the presence of an independent variable
List the scales of measurement from least informative to most informative -- Answer ✔✔ nominal - weakest (Sex, race, eye color) ordinal - (1st, 2nd, 3rd) interval - (temp) ratio - strongest (weight)
Operational Definition -- Answer ✔✔ A description of some observable event in terms of the specific process or manner by which is was observed or measured
True Zero -- Answer ✔✔ When the value zero truly indicates nothing on a scale of measurement. Interval scales do NOT have a true zero
Continuous Variable -- Answer ✔✔ Measured along a continuum
Discrete Variable -- Answer ✔✔ Whole units or categories
Quantitive Variable -- Answer ✔✔ Measured in numeric units
Qualitative Variable -- Answer ✔✔ Labels for the behaviors we observe

Sectors - particular portion of a pie chart that represents the relative percent of a particular class or category.

What is the difference in a histogram and a bar graph? -- Answer ✔✔ Histograms are made for continuous data while bar graphs are appropriate for discrete and categorical data
What letter identifies a population? A sample? -- Answer ✔✔ N = population size n = sample size
What is/are the measures of central tendency? -- Answer ✔✔ Statistical measures for locating a single score that is most representative or descriptive of all sets of scores in a distribution: the mean, the median, and the mode
Mean -- Answer ✔✔ the sum of the data, divided by the total number of scores
Median -- Answer ✔✔ the central score
Mode -- Answer ✔✔ the score that occurs the most
Define "skewed distribution" -- Answer ✔✔ a distribution of scores that includes outliers or scores that fall substantially above or below most other scores in a data set

Define variability -- Answer ✔✔ measure of the dispersion or spread of scores in a distribution and ranges from 0 to 1 Can't be negative
Identify three examples of variability -- Answer ✔✔ variance, standard deviation, range
Range -- Answer ✔✔ the difference between the largest value and the smallest value
Variance -- Answer ✔✔ measures the average squared distance that scores deviate from their mean
Standard Deviation -- Answer ✔✔ Represents the average amount of variability in a set of scores average distance from the mean
Population variance -- Answer ✔✔ o^
List the steps in calculating population variance -- Answer ✔✔ 1. Calculate the SS (the numerator)

Divide the SS by the population size (N)

Step 3: Compute the test statistic Step 4: Make a decision

What is the symbol for the null hypothesis? -- Answer ✔✔ Ho
What is the symbol for the alternative hypothesis? -- Answer ✔✔ Hi or Ha
What is a p-value? -- Answer ✔✔ probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true
What is a Type I error? -- Answer ✔✔ the probability of rejecting a null hypothesis that is actually true
What is a Type II error? -- Answer ✔✔ the probability of retaining a null hypothesis that is actually false
What is an effect size? -- Answer ✔✔ a statistical measure of the size of an effect in a population, which allows researchers to describe how far scores shifted in the population
How does an effect size differ from statistical significance? -- Answer ✔✔ depends on the sample size and effect size
What are the two ways to calculate an effect size? -- Answer ✔✔ 1. how far scores shifted in the population

the percent of variance that can be explained by a given variable

Define Cohen's d -- Answer ✔✔ measure of effect size in terms of the number of standard deviations that mean scores shifted above or below the population mean stated by the null hypothesis
What does Cohen's d measure? -- Answer ✔✔ the number of standard deviations an effect is shifted above or below the population mean (null hypothesis)
How do you interrupt Cohen's d? -- Answer ✔✔ when values of d are positive: an effect shifted above the population mean when values of d are negative: an effect shifted below the population mean
Define power -- Answer ✔✔ the likelihood of detecting an effect
What is the relationship between effect size and power? -- Answer ✔✔ as the effect size increases, power increases
What is the relationship between sample size and power? -- Answer ✔✔ as the sample size increases, power increases
What is needed in order to calculate a one sample z-test? -- Answer ✔✔ the population standard deviation/variance

Define random sampling -- Answer ✔✔ data being measured was obtained from a sample that was selected using a random sampling procedure
Define independence -- Answer ✔✔ each outcome or observations is independent, meaning one outcome does not influence another
What are the various effect sizes for a one-sample t test? What does each measure? -- Answer ✔✔ Cohen's d: uses sample standard deviations beta-squared: uses proportion of variance omega-squared: uses proportion of variance
How would you calculate confidence intervals for the one-sample t test? -- Answer ✔✔ using an estimated formula M+_ t(sM)
What is a Two-way ANOVA? -- Answer ✔✔ A statistical procedure used to test hypotheses concerning the variance of groups created by combining the levels of two factors
How does a two-way ANOVA differ from a one-way ANOVA? -- Answer ✔✔ By adding a second factor that will be observed in the same study
Give an example of a Two-way ANOVA -- Answer ✔✔ measure how quickly (in seconds) subjects respond to a stimulus that varies in size (small, medium, large) and color (bright, dark)

Why would a researcher add a second level in a research study? -- Answer ✔✔ 1. the hypothesis may require it

allows researchers to control or account for threats of validity

What is a factorial design? -- Answer ✔✔ research design for a study in which the levels of two or more factors are combined
Define between subjects two-way ANOVA -- Answer ✔✔ a type of factor in which different participants are observed at each level of one factor
Define within subjects two-way ANOVA -- Answer ✔✔ a type of factor in which the same participants are observed across the levels of one factor
Which significant result should the researcher analyze first? -- Answer ✔✔ analyze a significant interaction before analyzing a significant main effect
Define correlation. -- Answer ✔✔ used to identify the linear pattern or relationship between two variables
Define linear regression. -- Answer ✔✔ use the information from a correlation to predict values on one factor, given known values of a second factor use the value of a correlation to compute the equation of a regression line and then use this equation to predict values of one factor, given known factors of a second factor in a population

What is the coefficient of determination? -- Answer ✔✔ percentage of variance in one variable that is accounted for by the variance in another variable effect size for correlations square "r" to get r^
What is a correlation matrix? -- Answer ✔✔ way to illustrate results when you have more than two variables
What are the assumptions for a correlation? -- Answer ✔✔ 1. homoscedasticity

linearity
normality
causality

What is slope? -- Answer ✔✔ used to measure the change in the Y relative to the change in X
Define Y-intercept -- Answer ✔✔ the value of the criterion variable (Y) when the predictor variable (X) equals 0
What is negative slope? -- Answer ✔✔ values of Y decrease as values of X increase

What is positive slope? -- Answer ✔✔ values of Y increase as values of X increase
What is the difference between parametric and nonparametric? -- Answer ✔✔ Parametric: data on an interval or ratio measurement scale or normally distributed Nonparametric: data can be nominal or ordinal, often data is not normally distributed
What is a Chi-Squre test? -- Answer ✔✔ Statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies for the levels of a single categorical variable or two categorical variables observed together.
Define Chi-Squre Goodness-of-fit Test -- Answer ✔✔ Statistical procedure used to determine whether observed frequencies at each level of one categorical variable are similar to or different from the frequencies we expected at each level of the categorical variable
What is frequency observed? -- Answer ✔✔ count or frequency of participants recorded in each category or at each level of the categorical variable
What is frequency expected? -- Answer ✔✔ count or frequency of participants in each category, or at each level of the categorical variable, as determined by the proportion expected in each category

What does a two-independent sample t-test do? -- Answer ✔✔ test hypotheses concerning the difference between two population means, where the variance in one or both populations is unknown. compare scores/data between two groups Example: differences in multitasking between men and women
What are the assumptions of a two-independent-sample t-test? -- Answer ✔✔ 1. normality

random sampling
independence
equal variance

What are three examples of effect size for a two-independent-sample t-test? -- Answer ✔✔ estimated cohen's d, eta-squred, omega-squred
Define "related samples" design. What are the advantages of having a related- samples design? -- Answer ✔✔ participants are related, participants can be related in one of two ways: they are observed in more than one group, or they are matched, experimentally or naturally, based on common characteristics or traits. Advantages: more practical, reduces standard error, increases power
What are two types of related samples design? -- Answer ✔✔ The repeated- measures design The matched-pairs design
Which related samples design is the most common? -- Answer ✔✔ the repeated- measures design

What are the two types of repeated-measures design? -- Answer ✔✔ The pre- post design: measures a dependent variable for participants observed before (pre) and after (post) a treatment Within-subjects design: observe participants across many treatments but not necessarily before and after a treatment
What are two ways to have a matched-pairs design? -- Answer ✔✔ Experimental manipulation: the researcher manipulates the traits or characteristics upon which participants are matched Natural occurrence: the pre-existing traits are biological or physiological in nature
A t-test can only be used for what? -- Answer ✔✔ test differences in one group or between two groups
What is the symbol for a level of a factor/variable? -- Answer ✔✔ k
What is an Analysis of Variance? (ANOVA) -- Answer ✔✔ a statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means, where the variance in one or more populations is unknown
Define "n" and "N" for an ANOVA? -- Answer ✔✔ n= the number of participants per group N= the total number of participants in the study
What is an One-Way ANOVA? -- Answer ✔✔ test one factor with two or more levels concerning the variance among group means