Data Science Statistics Review

What type of statistical distribution allows us to model events where the outcome is discrete, and each outcome has an equally likely chance of occurring. For example, the probability that you flip heads or tails on a fair coin.

• Uniform Distribution

• Binomial Distribution

• Normal Distribution

• Poisson Distribution

Answer explanation

Which function would we use if we wanted to know the probability that a discrete random variable equals a specific value. For example, what is the probability that we roll a 3 on a die?

• Cumulative Density Function (cdf)

• Probability Mass Function (pmf)

• Survival Function (sf)

• Probability Density Function (pdf)

Answer explanation

This distribution allows us to model a situation where a certain number of events happen over a specified time interval. It is used to predict the amount of variation from a known average rate of occurrence within a given time frame. There is not a fixed number of events, so there is no ceiling on the number of events we can have.

• Uniform Distribution

• Binomial Distribution

• Normal Distribution

• Poisson Distribution

Which function would we use if we wanted to know the probability that a random variable is more than a specific value? For example, what is the probability that we roll a value greater than 3 on a die?

• Cumulative Density Function (cdf)

• Probability Mass Function (pmf)

• Survival Function (sf)

• Probability Density Function (pdf)

Answer explanation

Which of the following hypotheses would be considered the Alternative Hypothesis?

• Tomorrow's temperature will not be the same as today. (There is a relationship between temperature and day.)

• Tomorrow will be the same temperature as today. (There is no relationship between temperature and day.)

This distribution allows us to model a continuous random variable where the further away from the mean you are, the less likely the outcome. It is defined by a mean and a standard deviation. It is symmetric in shape, and the mean, median, and mode are equal.

• Uniform Distribution

• Binomial Distribution

• Normal Distribution

• Poisson Distribution

Answer explanation

Which type of t-test would we use if we wanted to find out if there is ANY difference between the means of two subgroups of a population? (a non-directional difference)

• one-sample, one-tailed t-test

• two-sample, two-tailed t-test

• one-sample, two-tailed t-test

• two-sample, one-tailed t-test

Answer explanation

Two-tailed means that we are interested in ANY significant difference in either direction or either tail of our distribution.

Which of the following are common assumptions we make when performing a t-test?

• Normality: normal distribution of data. Little skewness and no outliers.

• Sample Size: adequate sample size.

• Equality of Variance: similarity of variance throughout data. Standard deviations of sample are approximately equal

• Random Sample: data collected from representative, randomly selected portion of the total population.

• Independence of the observations: Each subject should belong to only one group. There is no relationship between the observations in each group.

What type of statistical test would we use if we want to find out if two continuous variables have a statistically significant relationship? Maybe we are looking at how hours studied relates to exam scores or how height relates to weight. (Examples: pearson r, spearman)

• chi-square test

• correlation test

• t-test

Which of the following hypotheses would be considered the Null Hypothesis?

• Tomorrow's temperature will not be the same as today. (There is a relationship between temperature and day.)

• Tomorrow will be the same temperature as today. (There is no relationship between temperature and day.)

Answer explanation

The null hypothesis states the "status quo". This hypothesis is assumed to be true until there is evidence to suggest otherwise.