STATS-131 Chapter 1 Quiz

What are the six steps of a statistical investigation?

1. Ask a research question 2. Design a study and collect data 3. Explore the data 4. Draw inferences 5. Formulate conclusions 6. Look back and ahead

What are the four pillars of statistical inference?

1. Significance 2. Estimation 3. Generalization 4. Causation

What are the 3 s's in the three s strategy?

1. Statistic 2. Simulation 3. Strength of evidence

What is a binary variable?

A categorical variable with only two outcomes.

What is a parameter?

A long run numerical property of the experiment process

What is a statistic?

A number summarizing the results of an experiment.

What is a Bell shaped curve?

A symmetrical distribution of scores.

What is a quantitative variable?

A variable measured in numbers

What is a categorical variable?

A variable measured in words: (I.e yes or no, or right-eyed vs left-eyed)

What do H0 and Ha stand for?

H0 is the null hypothesis and Ha is the alternative hypothesis.

What is the central limit theorem?

If a sample size is large enough, the distribution of sample proportions will be bell-shaped, centered at the long-run proportion, with a standard deviation of square root of (pi(1-n)/n

What are validity conditions?

In order for a simulation or experiment to be valid, it must have at least 10 successes and 10 failures.

What does a two-sided test do to the p-value?

It almost doubles the size of the p-value, which decreases the strength of evidence against the null hypothesis.

What does increasing the sample size do to the strength of evidence?

It increases the strength of evidence.

What is the z-statistic?

It is the standardized statistic.

What do we use pi for in statistics?

It represents a parameter that is a probability. (i.e. a 0.3 or a 0.5 chance of a result.) Another way of putting it is your probability of success.

What is the theory-based approach?

It standardizes the statistic based on the observed value of the statistic and the theoretical mean and standard deviation values.

Can we ever prove a null hypothesis false?

No, because we are assuming the null is true to get the alternative hypothesis.

What does it mean for something to be plausible?

Simply that it is possible or believable.

What does it mean for a result to be statistically significant?

That the result is unlikely to happen by random chance.

What is a two-sided test?

The alternative hypothesis looks at both sides of the parameter and says that the chance of getting our result might be more or it might be less.

What is a null hypothesis?

The hypothesis that the results you are getting are by chance.

What is an alternative hypothesis?

The hypothesis that there is something more than chance going on.

What does the theory-based approach predict?

The null distribution will be bell-shaped and approximately normal The null distribution will be centered around the mean The standard deviation will follow the theory-based formula for standard deviations.

What is the sample size?

The number of observational units within a sample.

What is a standardized statistic?

The number of standard deviations our statistic is away from the center/mean of our simulation data.

What is the p-value?

The probability of obtaining a value of the statistic at least as extreme as the observed statistic when the null hypothesis is true. We can estimate the p-value by finding the proportion of the simulated statistics in the null distribution that are at least as extreme as the value of the statistic actually observed in the research study.

What do we use p-hat used for in statistics?

The proportion of times you are getting a result. (if 9 people out of 17 are right handed, your p-hat would be 9/17 or 0.53)

What does the letter "n" represent in statistics?

The sample size.

What is a sample?

The set of observational units on which we are collecting data

What does the p-value tell us about our statistic?

The smaller the p-value, the greater the evidence against the null hypothesis. The bigger the p-value, the weaker the evidence against the null hypothesis.

What is a variable?

The thing we are changing within the experiment to get different results. (For example, in the experiment to see if more people are right handed, the variable is whether or not they are right or left eyed.)

When can we consider a statistic to be in the tail of the distribution?

When it is 2 or 3 standard deviations or more away from the center/mean of our simulation data.