Quantitative Quiz 17MarkMarch 7, 2025Quantitative Aptitude Welcome to your Quantitative Quiz 17 What does the central limit theorem state? The sample mean approaches the population mean as the sample size increases The distribution of sample means approaches a normal distribution as the sample size increases The sample standard deviation approaches the population standard deviation as the sample size increases The population distribution becomes normal with large sample sizes None Which of the following is the definition of "bias" in statistical estimation? The difference between the sample mean and population mean The tendency of a sample statistic to systematically over- or under-estimate the population parameter The variability in the sample statistic The difference between observed and expected outcomes None What does the term "heteroscedasticity" refer to in regression analysis? The variance of the residuals is constant across all levels of the independent variable The variance of the residuals is not constant across all levels of the independent variable The data points follow a normal distribution The relationship between the dependent and independent variables is non-linear None Which test would you use to compare the means of more than two independent groups? One-way ANOVA Paired T-test Two-sample T-test Chi-square test None Which of the following distributions is typically used for modeling the time between events in a Poisson process? Normal distribution Exponential distribution Binomial distribution Poisson distribution None What is the key assumption in linear regression analysis? The relationship between the dependent and independent variables is linear The dependent variable is categorical There are no outliers in the dataset The independent variables are not correlated with each other None Which of the following is the primary purpose of a hypothesis test? To describe the characteristics of a population To estimate a population parameter To test the validity of a hypothesis about a population To predict future data points None In probability theory, which of the following describes an event that can never occur? A mutually exclusive event An impossible event A complementary event A random event None Which of the following statistical tests is used to compare two independent groups? Paired T-test One-way ANOVA Two-sample T-test Chi-square test None What is the primary goal of regression analysis? To compare the means of two groups To estimate the relationship between variables To calculate the variance of a sample To test the null hypothesis None Which of the following is true for a chi-square distribution? It is symmetric and bell-shaped It is used to model continuous variables It is used to analyze the relationship between categorical variables It has a negative skew None What does a p-value less than 0.05 indicate in hypothesis testing? There is strong evidence to reject the null hypothesis The null hypothesis is true There is insufficient evidence to reject the null hypothesis The test is invalid None What is the significance of the p-value in hypothesis testing? It represents the probability that the null hypothesis is true It indicates the strength of the evidence against the null hypothesis It measures the difference between the observed and expected values It determines the power of the test None Which of the following best describes a negatively skewed distribution? The right tail is longer than the left tail The distribution is symmetric The left tail is longer than the right tail The mean is greater than the median None Which of the following is an example of a continuous probability distribution? Binomial distribution Poisson distribution Normal distribution Hypergeometric distribution None In a normal distribution, approximately what percentage of the data falls within one standard deviation of the mean? 68% 95% 99% 50% None Which of the following tests is used to determine the relationship between two categorical variables? T-test Chi-square test for independence Z-test Paired T-test None What does the term "outlier" refer to in a dataset? A value that is within one standard deviation of the mean A value that falls far outside the normal range of the data A value that is equal to the median A value that is exactly equal to the mean None What does the term "statistical power" refer to? The probability of rejecting a false null hypothesis The ability to accept the null hypothesis The probability of making a Type I error The strength of the correlation between two variables None Which of the following best describes a Type I error in hypothesis testing? Rejecting a true null hypothesis Failing to reject a false null hypothesis Incorrectly concluding that there is no effect Accepting the null hypothesis when it is false None What is the main difference between a population and a sample? A population includes all members of a group, while a sample is a subset of the population A population is always larger than a sample A sample includes all members of a group, while a population is a subset A population is used in hypothesis testing, while a sample is not None What does a confidence interval represent? The probability that the sample mean is within a specific range A range of values that is likely to contain the population parameter with a certain level of confidence The probability of making a Type I error A range of values that is likely to contain the population parameter with a certain level of None What is the primary purpose of the z-test in statistics? To compare the means of two independent groups To test the hypothesis about the population mean when the population variance is known To compare the variances of two populations To calculate the correlation between two variables None In probability theory, which of the following represents the likelihood of an event occurring? Mean Probability Standard deviation Variance None Which of the following is true about the standard normal distribution? The mean is 1 The standard deviation is 0 The mean is 0 and the standard deviation is 1 The distribution is skewed None What is the primary purpose of a p-value in hypothesis testing? To measure the strength of the relationship between two variables To determine the probability that the null hypothesis is true To test whether the sample data supports the null hypothesis To estimate the population parameter None Which of the following is an example of an ordinal variable? Age Temperature Education level (e.g., high school, bachelor's, master's) Weight None Which of the following would be most appropriate for testing the difference between the means of two unrelated groups? Paired t-test Independent samples t-test One-way ANOVA Chi-square test None What is the assumption made in the hypothesis test for a population mean using the z-test? The population mean is unknown The population standard deviation is known The sample is not random The sample size is smaller than 30 None None 1 out of 6 Time's upTime is Up! Post Views: 188
