The lifetime of a certain electronic component follows an exponential distribution with a mean of 10,000 hours. What is the probability that a randomly selected component lasts less than 5,000 hours?
0.3935
0.6321
0.5
0.25
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
0.05
0.57
0.996
When would you use a paired t-test instead of an independent t-test?
When comparing the means of two groups with unequal variances.
When comparing the means of two independent groups.
When comparing the means of three or more groups.
When comparing the means of the same group before and after a treatment.
What is the primary purpose of inferential statistics?
To organize and clean raw data.
To describe and summarize data.
To make generalizations about a population based on a sample.
To visually represent data using graphs and charts.
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
One-sample t-test
Chi-square test
Independent samples t-test
Paired t-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?
0.3
Cannot be determined
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
3/5
2/5
3/4
A Chi-square test is used to:
Analyze the variance within and between groups.
Compare the means of two groups.
Analyze the relationship between two categorical variables.
Determine if a sample mean is significantly different from a known population mean.
What is the purpose of calculating a correlation coefficient?
To test the significance of the difference between two means.
To measure the strength and direction of the linear relationship between two variables.
To determine the cause-and-effect relationship between two variables.
To predict the value of one variable based on the value of another variable.
Which component of a time series reflects long-term changes in the data over time?
Seasonality
Trend
Irregularity
Cyclical Variation