AP Statistics

If I increase my sample size, what will happen to my confidence interval? My standard deviation? My Mean? My point estimate? My margin of error?

As the sample size increases, the confidence interval will become narrower, indicating more precision in the estimate. The standard deviation may remain unchanged, but the standard error will decrease, leading to a smaller margin of error. The mean and point estimate will likely stabilize around the true population parameter.

If I have an observational study, can I generalize? If I have an experiment, can I generalize?

In an observational study, generalization can be limited due to lack of control over variables, making it harder to establish causation. In an experiment, if properly randomized and controlled, generalization is more valid, allowing for stronger inferences about the population.

What can make an experiment generalizable?

Randomization, control over variables, and representative sampling.

How do I know if I need to use a bar graph? Histogram? Dot plot?

Bar Graph: use when comparing categorical data.

Histogram: Use when showing the distribution of numerical data.

Dot plot: Dot plots are used for small to moderate-sized data sets and are useful for highlighting clusters, gaps, and outliers.

If we removed an outlier on a linear regression model, what will happen?

The regression line may shift, resulting in a better fit for the remaining data and potentially altering the slope and intercept of the model.

Define “power of the test”

The power of the test refers to the probability that the test will correctly reject a false null hypothesis, thus avoiding a Type II error. It is influenced by the sample size, effect size, and significance level.

If we increase our sample size what happens to our significance level AND our power of the test?

Increasing the sample size generally increases the power of the test, making it easier to detect a true effect. However, the significance level remains unchanged, as it is determined by the predefined threshold (e.g., 0.05) for rejecting the null hypothesis.

What’s the random variable of interest?

The random variable of interest is the quantity or outcome being measured or observed in a statistical analysis, often represented by a symbol such as X. It can take on different values based on the results of random phenomena.

How can random variables of interest be distributed?

Random variables can be distributed according to various probability distributions, such as the normal distribution, binomial distribution, or Poisson distribution, depending on the nature of the data and the underlying processes.

When do you use segmented bar charts?

Segmented bar charts are used when comparing the proportion of different categories within a total across various groups. They effectively display the relationship between categorical variables and help in visualizing data distributions.

“Is the researchers claim correct” —> Is this confidence interval or significant test>

A hypothesis test is used to determine if the researcher’s claim is correct, often involving the evaluation of p-values and confidence intervals.