statistical inference Flashcards
What is statistical inference?
The process of drawing conclusions about a population based on a sample.
True or False: Statistical inference can only be performed with large sample sizes.
False.
Fill in the blank: A _______ is a numerical summary of a sample.
statistic
What is a population in statistical terms?
The entire group of individuals or instances about whom we hope to learn.
What is a sample?
A subset of the population selected for analysis.
Multiple Choice: Which of the following is a common method for selecting a sample?
Random sampling.
What is the purpose of hypothesis testing?
To determine whether there is enough evidence to reject a null hypothesis.
True or False: The null hypothesis typically represents a statement of no effect or no difference.
True.
Fill in the blank: The _______ is the probability of making a Type I error.
alpha level
What is a Type I error?
Rejecting the null hypothesis when it is actually true.
What is a Type II error?
Failing to reject the null hypothesis when it is false.
Multiple Choice: Which of the following is a common significance level used in hypothesis testing?
0.05.
What does p-value represent?
The probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
True or False: A smaller p-value indicates stronger evidence against the null hypothesis.
True.
What is confidence interval?
A range of values derived from a sample that is likely to contain the value of an unknown population parameter.
Fill in the blank: A 95% confidence interval means that if we were to take many samples, _______ of those intervals would contain the true population parameter.
95%
What is the Central Limit Theorem?
The theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases.
True or False: The Central Limit Theorem applies only to normally distributed populations.
False.
What is a point estimate?
A single value estimate of a population parameter.
Multiple Choice: Which of the following is NOT a method of estimation?
Extrapolation.
What is the difference between descriptive statistics and inferential statistics?
Descriptive statistics summarize data, while inferential statistics draw conclusions about a population based on sample data.
Fill in the blank: A _______ is a graphical representation of the distribution of a dataset.
histogram
What is the purpose of a t-test?
To determine if there is a significant difference between the means of two groups.
True or False: The t-test can only be used for normally distributed data.
False.
What is ANOVA?
Analysis of Variance, a method used to compare means among three or more groups.
Multiple Choice: Which of the following is a prerequisite for conducting ANOVA?
Independence of observations.
What is a chi-square test used for?
To determine if there is a significant association between categorical variables.
Fill in the blank: The _______ test is used to compare observed frequencies with expected frequencies.
chi-square
True or False: Correlation implies causation.
False.
What does a correlation coefficient of 1 indicate?
A perfect positive linear relationship between two variables.
What does a correlation coefficient of -1 indicate?
A perfect negative linear relationship between two variables.
Multiple Choice: What is the range of values for a correlation coefficient?
-1 to 1.
What is regression analysis used for?
To model the relationship between a dependent variable and one or more independent variables.
Fill in the blank: In regression analysis, the _______ variable is the one being predicted.
dependent
True or False: In linear regression, the relationship between variables is assumed to be linear.
True.
What is multicollinearity?
A situation in regression analysis where independent variables are highly correlated.
What is the purpose of the residual analysis in regression?
To check the validity of the regression model by analyzing the differences between observed and predicted values.
Multiple Choice: Which of the following is a common criterion for model selection in regression?
Adjusted R-squared.
What is the difference between parametric and non-parametric tests?
Parametric tests assume a specific distribution, while non-parametric tests do not.
Fill in the blank: Non-parametric tests are often used when data does not meet _______ assumptions.
normality
What is the role of sample size in statistical inference?
Larger sample sizes generally provide more reliable estimates and reduce sampling error.
True or False: Increasing the sample size can decrease the margin of error.
True.
What is the importance of random sampling?
It helps ensure that the sample is representative of the population, reducing bias.
Multiple Choice: Which of the following is a common misconception about statistical significance?
Statistical significance implies practical significance.
What is a power analysis?
A method used to determine the sample size required to detect an effect of a given size with a certain degree of confidence.
Fill in the blank: The _______ is the probability of correctly rejecting the null hypothesis.
power
What is effect size?
A quantitative measure of the magnitude of a phenomenon.
True or False: Effect size can help to interpret the practical significance of a result.
True.
What does the term ‘sampling distribution’ refer to?
The probability distribution of a statistic obtained from a large number of samples drawn from a specific population.
Multiple Choice: Which of the following is a key assumption of linear regression?
Linearity of relationships.
What is the significance of the F-test in ANOVA?
It tests whether there are significant differences between group means.
Fill in the blank: The _______ is a summary measure that describes the strength and direction of a linear relationship between two variables.
correlation coefficient
What is a confidence level?
The percentage of times that a confidence interval would contain the true population parameter if the same sampling method were repeated.
True or False: A 99% confidence interval is wider than a 95% confidence interval.
True.
