What is the primary purpose of inferential statistics?
To describe and summarize data.
To make generalizations about a population based on a sample.
To visually represent data using graphs and charts.
To organize and clean raw data.
In multiple regression, what does a high variance inflation factor (VIF) indicate?
A good fit of the regression model
Low multicollinearity among predictor variables
High multicollinearity among predictor variables
Heteroscedasticity in the residuals
What does a p-value less than the significance level (alpha) indicate?
There is strong evidence to reject the null hypothesis.
The null hypothesis should be accepted.
The alternative hypothesis is proven true.
There is insufficient evidence to reject the null hypothesis.
Which of the following is NOT a key assumption of the Central Limit Theorem?
The population distribution is normal.
The sample size is sufficiently large (generally n ≥ 30).
The population has a finite mean and variance.
The samples are independent and randomly selected.
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
Residuals consistently increasing with increasing values of the independent variable
Randomly scattered residuals
A curved pattern in the residuals
All residuals clustered around zero
What is the purpose of using a correlation matrix in multivariate statistics?
To visualize the distribution of residuals in regression
To assess the strength and direction of linear relationships between pairs of variables
To determine the optimal number of factors in factor analysis
To identify outliers in a dataset
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Zero
Higher
Lower
Equal
In a binomial distribution, if the probability of success on each trial is 0.3 and there are 10 trials, what is the expected value of the number of successes?
7
5
10
3
Suppose 60% of emails in your inbox are spam and 40% are legitimate. Also, 95% of spam emails contain the word 'free,' while only 1% of legitimate emails do. If an email contains the word 'free,' what's the probability it's spam?
0.996
0.004
0.57
0.05
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
There is a 95% probability that the true population mean falls between 60 and 80.
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
We are 95% confident that the sample mean falls between 60 and 80.
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.