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
Chi-square test
Independent samples t-test
What is the purpose of using a correlation matrix in multivariate statistics?
To visualize the distribution of residuals in regression
To identify outliers in a dataset
To assess the strength and direction of linear relationships between pairs of variables
To determine the optimal number of factors in factor analysis
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 is the null hypothesis in a Chi-square test of independence?
The two variables are independent.
The two variables are dependent.
The means of the two groups are equal.
The variances of the two groups are equal.
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
Cannot be determined
0.3
0.5
Let X be a random variable representing the number of heads when you toss a fair coin three times. What is the variance of X?
0.75
1
1.5
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?
ANOVA
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?
0.004
0.57
0.996
0.05
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
0.6875
0.3125
0.25
When is ANOVA (Analysis of Variance) used instead of a t-test?
When comparing the means of two groups.
When analyzing the relationship between two categorical variables.
When comparing the means of three or more groups.
When comparing the variances of two groups.