What is the primary purpose of inferential statistics?
To organize and clean raw data.
To visually represent data using graphs and charts.
To describe and summarize data.
To make generalizations about a population based on a sample.
A bag contains 3 red balls and 2 blue balls. You draw two balls from the bag without replacement. What is the probability that the second ball is red, given that the first ball was blue?
3/4
3/5
2/5
1/4
What is the primary difference between simple exponential smoothing and double exponential smoothing?
Simple exponential smoothing uses a moving average, while double exponential smoothing uses an autoregressive model.
Double exponential smoothing considers trend, while simple exponential smoothing does not.
Simple exponential smoothing considers seasonality, while double exponential smoothing does not.
Double exponential smoothing is used for stationary data, while simple exponential smoothing is used for non-stationary data.
If the variance of a random variable is 9, what is its standard deviation?
18
81
9
3
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
There is a 95% probability that the true population mean falls 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.
What does an R-squared value of 0.80 indicate?
The correlation between the variables is 0.80.
The slope of the regression line is 0.80.
20% of the variation in the dependent variable is explained by the independent variable.
80% of the variation in the dependent variable is explained by the independent variable.
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?
0.004
0.57
0.05
0.996
Which of the following statements is TRUE about multivariate analysis of variance (MANOVA)?
It examines the relationship between two continuous variables.
It is used for dimensionality reduction of categorical variables.
It tests the difference in means between two groups on a single dependent variable.
It analyzes the differences between groups on multiple dependent variables simultaneously.
A Chi-square test is most appropriate for analyzing which type of data?
Continuous data
Categorical data
Time series data
Normally distributed data
A Chi-square test is used to:
Determine if a sample mean is significantly different from a known population mean.
Analyze the relationship between two categorical variables.
Compare the means of two groups.
Analyze the variance within and between groups.