Sampling and Bias
What is the process of selecting a subset of individuals from a larger population called?
Sampling.
What is a range of values constructed around a sample proportion to estimate an unknown population proportion called?
Confidence interval.
What is the process of making a decision about a population based on sample data called?
Hypothesis testing.
What is the difference between the sample proportions of two groups in a hypothesis test for two proportions?
The observed difference in sample proportions.
What is the purpose of conducting a hypothesis test for proportions?
The purpose is to determine if there is statistically significant evidence to support a claim or hypothesis about a population proportion.
What bias occurs when a survey asks people to report on their own actions or opinions called?
Response Bias.
What is the level of confidence typically expressed as when constructing a confidence interval?
A percentage (e.g., 95% confidence interval).
What are the two competing hypotheses in hypothesis testing?
The null hypothesis and the alternative hypothesis.
What is the formula for the standard error in a hypothesis test for two proportions?
Standard Error = √[(p₁ * (1 - p₁))/n₁ + (p₂ * (1 - p₂))/n₂]. (I know its ugly)
How is the test statistic calculated in a hypothesis test for proportions?
The test statistic, often denoted as z or t, is calculated by standardizing the difference between the sample proportion and the hypothesized proportion.
What bias can occur when a survey asks people questions by email called?
Undercoverage Bias/Non-Response Bias.
What is the formula for the margin of error in a confidence interval for a proportion?
The margin of Error = (critical value) * (standard error).
What is the name for the probability of observing a sample result as extreme as, or more extreme than, the one obtained if the null hypothesis is true?
P-value.
What is the null hypothesis in a hypothesis test for two proportions?
The null hypothesis states that there is no difference between the proportions of the two groups.
What is the critical value in a hypothesis test for proportions?
The critical value is the value(s) that separates the rejection region from the non-rejection region in a hypothesis test.
What bias can occur when a survey that collects data by sending questionnaires to a sample of individuals happens?
Non-Response Bias.
True or False: A larger sample size leads to a smaller margin of error in a confidence interval.
True.
If the P-value is less than the significance level (α), do we reject or fail to reject the null hypothesis?
We reject the null hypothesis.
How many degrees of freedom are associated with a hypothesis test for two proportions?
The degrees of freedom depends on the sample sizes and can be calculated as (n₁ - 1) + (n₂ - 1).
What is a Type I error in hypothesis testing for proportions?
A Type I error occurs when the null hypothesis is rejected, but it is actually true in the population.
What is the term for the part of the population that is actually selected to be surveyed?
Sample.
What is the term for the maximum amount by which a confidence interval is expected to vary due to random sampling error?
The term is "margin of error."
DOUBLE JEOPARDY!!! (Add 2x points for this one)
How is the significance level (α) related to the probability of making a Type I error in hypothesis testing?
The significance level is the probability of making a Type I error.
If the confidence interval for the difference in proportions includes zero, what does it suggest about the two proportions?
It suggests that there is no statistically significant difference between the proportions of the two groups.
How is the p-value interpreted in hypothesis testing for proportions?
The p-value represents the probability of obtaining a sample proportion as extreme as the observed proportion, assuming the null hypothesis is true.