When is Spearman's rank correlation a more appropriate measure of association than Pearson's correlation?
When the relationship between variables is non-linear but monotonic
When outliers are not present in the data
When the variables are measured on an interval or ratio scale and normally distributed
When the relationship between variables is perfectly linear
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
Paired t-test
One-sample t-test
Independent samples t-test
Chi-square test
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?
0.7
0.5
Cannot be determined
0.3
What is the range of the Pearson correlation coefficient?
0 to infinity
0 to 1
-1 to 0
-1 to 1
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Lower
Zero
Higher
Equal
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?
0.4
A Chi-square test is most appropriate for analyzing which type of data?
Normally distributed data
Categorical data
Continuous data
Time series data
What is the primary purpose of inferential statistics?
To make generalizations about a population based on a sample.
To organize and clean raw data.
To visually represent data using graphs and charts.
To describe and summarize data.
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
All residuals clustered around zero
Residuals consistently increasing with increasing values of the independent variable
A curved pattern in the residuals
Randomly scattered residuals
A normal distribution has a mean of 50 and a standard deviation of 10. What is the probability that a randomly selected value from this distribution is between 40 and 60?
0.6827
0.9973
0.3413
0.9545