Probability and Statistics
Researchers want to test a new anti-anxiety medication by splitting participants into three conditions: 0 mg, 50 mg, and 100 mg, then asking them to rate their anxiety on a scale of 1 to 10. Are there any differences between the three conditions using an alpha of 0.05?
Investigate whether there is a difference between fertilizers A, B, and C in terms of plant growth using a one-way ANOVA.
Determine whether three different drugs have a different effect on blood pressure using a one-way ANOVA.
Solve a one-way ANOVA problem given the data of a sample size of 24 divided into three groups, using blood pressure readings before and after treatment.
Using the one-way ANOVA method, test the null hypothesis that K populations all have the same mean by comparing the variability between groups to the variability within groups.
Using the data in the table, calculate the correlation coefficient to measure the strength of the relationship between the average length of schooling and life expectancy of the population.
Perform a linear regression on the data and analyze the type of correlation based on the value of the correlation coefficient .
Using the ANOVA method, determine if there is a statistically significant difference in age among users of different statistical software, specifically Data Tab, SPSS, and R.
You want to find out if the beverage that people drink affects their reaction time. Set up an experiment with three groups of people. The first group gets water to drink. The second group gets some sugary fruit juice, and the third group gets coffee. Test everyone's reaction time and determine if there's any difference in reaction time between the groups using the analysis of variance.
A factory has two machines, A and B. Machine A produces 60% of the items, while Machine B produces 40%. 2% of the items produced by Machine A are defective, while 3% of the items produced by Machine B are defective. If a randomly selected item is found to be defective, what is the probability it was produced by Machine B?
A software company has two teams, Team A and Team B. Team A completes 60% of projects, and Team B completes 40%. Team A has a 90% success rate, and Team B has an 80% success rate. If a project is successful, what is the probability it was completed by Team B?
In a certain city, 30% of the population has a certain disease. A test for the disease is 90% accurate (true positive rate), and has a 10% false positive rate. If a person tests positive, what is the probability that they actually have the disease?
What's the probability that someone has a college degree given they voted?
Find the probability of rolling a 1 exactly twice in four rolls of a fair six-sided die.
What are the probabilities of collecting six frogs, determining their sexes, and getting a result in which there are zero males, one male, two males, etc., from those six frogs?
In a game of roulette, spin the wheel three times and determine the probabilities of the ball landing in an even pocket zero, one, two, or three times.
What are the probabilities of collecting six frogs, determining their sexes and getting a result in which there are zero males, one male, two males, etc., from those six frogs?
In a game of roulette, spin the wheel three times and determine the probabilities of the ball landing in an even pocket zero, one, two, or three times.
For our example, we're going to be taking a look at years of teaching experience. So ten teachers were surveyed, and here are the results. Again, this is years of teaching experience.
What is the probability that a random selection of 32 women have an average age at first marriage between 26 and 27?