If the variance of a random variable is 9, what is its standard deviation?
9
81
3
18
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.
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
We are 95% confident that the sample mean falls between 60 and 80.
A researcher wants to determine if a new drug reduces blood pressure more effectively than a placebo. They measure the blood pressure of the same group of patients before and after taking the drug and placebo (in random order). What test should they use?
One-sample t-test
Paired t-test
ANOVA
Independent samples t-test
Principal Component Analysis (PCA) is primarily a ______ technique.
Regression
Clustering
Classification
Dimensionality Reduction
What does a Pearson correlation coefficient of -0.9 suggest about the relationship between two variables?
No linear relationship
Weak positive linear relationship
Strong negative linear relationship
Strong positive linear relationship
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
0.57
0.05
0.004
In ANOVA, what does the F-statistic represent?
The correlation coefficient between the independent and dependent variables.
The difference between the smallest and largest group means.
The ratio of between-group variance to within-group variance.
The probability of observing the data if all group means were equal.
What is the primary difference between simple exponential smoothing and double exponential smoothing?
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.
Simple exponential smoothing uses a moving average, while double exponential smoothing uses an autoregressive model.
In simple linear regression, what does the slope of the regression line represent?
The change in the dependent variable for a one-unit change in the independent variable
The point where the regression line crosses the y-axis
The strength of the relationship between the variables
The average value of the dependent variable
Which of the following is NOT a key assumption of the Central Limit Theorem?
The samples are independent and randomly selected.
The population distribution is normal.
The sample size is sufficiently large (generally n ≥ 30).
The population has a finite mean and variance.