A high R² value in a regression analysis always indicates a good fit of the model. Is this statement true or false?
True
False
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
0.3
0.5
0.7
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?
1/4
2/5
3/5
3/4
A moving average model is best suited for forecasting time series data with which characteristic?
High volatility
A constant mean
Significant outliers
Strong seasonality
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
We are 95% confident that the sample mean falls between 60 and 80.
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.
Which of the following is an example of a non-parametric inferential statistical test?
ANOVA
z-test
Chi-square test
t-test
When would you use a paired t-test instead of an independent t-test?
When comparing the means of two independent groups.
When comparing the means of three or more groups.
When comparing the means of two groups with unequal variances.
When comparing the means of the same group before and after a treatment.
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
What is a Type II error in hypothesis testing?
Using the wrong test statistic for the data.
Rejecting the null hypothesis when it is true.
Incorrectly calculating the p-value.
Failing to reject the null hypothesis when it is false.
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?
0.57
0.004
0.996
0.05