G2 Probability and Statistics Final Exam Review

Front

Why is it important to calculate the spread as well as the mean for a data set?

Back

The spread provides information about the variability of the data, while the mean only shows the center. We should know how spread out the data is in order to give us an overall picture of the data set.

Front

What are the properties of a binomial experiment?

Back

B- Binary, success or failure; I- Independent, trials are independent; N- Number of trials is fixed; S- Same probability.

Front

Under what conditions does the sampling distribution approximate the normal distribution for means and proportions?

Back

For means: The sampling distribution of the sample mean approximates a normal distribution if the population is normally distributed or the sample size is large (n ≥ 30) due to the Central Limit Theorem. For proportions: The sampling distribution of the sample proportion is approximately normal if both n(p)≥10 and n(1−p)≥10.

Front

How do we know when to fail to reject/reject the null hypothesis in a significance test?

Back

Use the p-value and compare it to the significance level (usually α=0.05). Reject the null hypothesis if p ≤ α; Fail to reject the null hypothesis if p ≥ α.

Front

Explain the null hypothesis and the alternative hypothesis in significance testing.

Back

The null hypothesis is the starting assumption and the alternative hypothesis is what you want to prove.

Front

When given raw data and asked to perform a statistical analysis on it, how should you first examine the data? What are you looking for?

Back

Understand the purpose of the data and what it all means by its context. Then, look at statistics like mean, minimum, and maximum, range, and standard deviation to get a feel for the data. Then, check for outliers that don’t make sense and create charts or graphs to see patterns, trends and differences and form conclusions.

Front

What are the measures of center of data? When would each be used?

Back

Mean & median. Median is used when there’s an outlier or skew, mean is used when the data has no outliers or skew.

Front

What are the steps in the simulation of an event?

Back

State the Problem or Question Clearly; Assign Outcomes to Random Digits or Tools; Simulate one trial and repeat; Analyze results and draw conclusion.

Front

Why, when we run several trials, is the observed probability not always equal to the theoretical probability?

Back

As the number of trials increases, the observed probability tends to get closer to the theoretical probability. With only a few trials, there isn’t enough data for this law to take effect.

Front

What is the difference between a discrete and continuous random variable?

Back

The difference between discrete and continuous random variable is that a discrete random variable is countable with distinct value and a continuous is any given value (all possible decimals) within a range.