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.
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
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.
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?
3/5
2/5
3/4
1/4
When would you use a paired t-test instead of an independent t-test?
When comparing the means of three or more groups.
When comparing the means of two independent groups.
When comparing the means of the same group before and after a treatment.
When comparing the means of two groups with unequal variances.
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
In multiple regression, what does a high variance inflation factor (VIF) indicate?
Heteroscedasticity in the residuals
A good fit of the regression model
High multicollinearity among predictor variables
Low multicollinearity among predictor variables
What is a Type II error in hypothesis testing?
Incorrectly calculating the p-value.
Using the wrong test statistic for the data.
Rejecting the null hypothesis when it is true.
Failing to reject the null hypothesis when it is false.
What does a p-value less than the significance level (alpha) indicate?
The null hypothesis should be accepted.
There is strong evidence to reject the null hypothesis.
The alternative hypothesis is proven true.
There is insufficient evidence to reject the null hypothesis.
Which of the following smoothing methods is most appropriate when the time series data exhibits a trend but no seasonality?
Moving Average Smoothing
Simple Exponential Smoothing
Double Exponential Smoothing
Triple Exponential Smoothing
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Equal
Lower
Zero
Higher
Which of the following is NOT an assumption of linear regression?
Independence of observations
Normality of the independent variable
Linearity of the relationship between independent and dependent variables
Homoscedasticity (equal variance of errors)