A random variable follows a uniform distribution between 0 and 10. What is the probability that the variable takes a value between 3 and 7?
0.7
0.5
0.3
0.4
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.
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.
You're playing a game where you flip a coin. Heads, you win $10. Tails, you lose $5. What is the expected value of playing this game?
$0.00
$5.00
-$2.50
$2.50
In ANOVA, what does the F-statistic represent?
The difference between the smallest and largest group means.
The probability of observing the data if all group means were equal.
The ratio of between-group variance to within-group variance.
The correlation coefficient between the independent and dependent variables.
In PCA, what does a scree plot help determine?
The optimal number of principal components to retain
The amount of variance explained by each variable
The correlation between principal components
The presence of multicollinearity
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?
Paired t-test
Independent samples t-test
One-sample t-test
ANOVA
What is a key assumption of autoregressive models?
The data is free from outliers and missing values.
There is no correlation between past and future values.
The time series data exhibits strong seasonality.
The data has a constant mean and variance over time.
An event has three possible outcomes: A, B, and C. You know P(A) = 0.2 and P(B) = 0.3. What is the value of P(C) according to the law of total probability?
Cannot be determined
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?
10
7
5
3
In an AR(p) model, what does 'p' represent?
The smoothing parameter.
The number of future time steps to forecast.
The number of past time periods used for prediction.
The seasonality index.