The probability of a Type I error, chosen by the researcher before the data are analyzed, is denoted by the Greek letter alpha.
Missing Word
alpha
Alpha is the significance level of a test, the probability of rejecting a null hypothesis that is true. It is set in advance, commonly at 0.05 or 0.01.
Category: Type I and II Errors
Question 2
The probability of not detecting that a null hypothesis is false, a Type II error, is denoted by the Greek letter beta.
Missing Word
beta
Beta is the probability of a Type II error, failing to reject a false null hypothesis. It depends on the sample size, alpha, and how far the truth is from the null value.
Category: Type I and II Errors
Question 3
The probability that a test correctly rejects a false null hypothesis, equal to 1 minus the Type II error probability, is called the power of the test.
Missing Word
power
Power measures a test's ability to detect a real effect. Larger samples raise it, and researchers want it as close to 1 as possible.
Category: Type I and II Errors
Question 4
The hypotheses in a test are always statements about a population parameter, never about a value computed from the sample.
Missing Word
parameter
A parameter is a numerical characteristic of a population, such as a population mean or proportion. Hypotheses concern parameters because the goal is to learn about the population, not to describe the sample already in hand.
Category: Setting Up Hypotheses
Question 5
A z test of a claim such as 'more than 30% of adults own a bike' relies on the normal approximation to the binomial distribution.
Missing Word
binomial
The number of successes in a sample is binomial, and with a large enough sample the binomial distribution is close to normal. That approximation lets a one-proportion test use z-scores.
Category: Choosing the Distribution
Question 6
Using sample data to draw conclusions about a whole population, through tools such as hypothesis tests and confidence intervals, is called statistical inference.
Missing Word
inference
Statistical inference means reaching conclusions about a population from sample evidence. Hypothesis tests and confidence intervals are its two main tools, and both account for the chance variation from sample to sample.
Category: Setting Up Hypotheses
Question 7
Hypotheses about a population mean use the Greek letter mu to stand for the true mean.
Missing Word
mu
Mu is the symbol for a population mean, as in H0: mu = 50. The sample mean, written x-bar, is used to estimate it.
Category: Setting Up Hypotheses
Question 8
Because it is built on the sample mean and sample standard deviation, a one-sample t test with a small sample can be badly distorted by a few extreme values, called outliers.
Missing Word
outliers
Outliers are values far from the rest of the data. In a small sample, even one outlier can shift x-bar and inflate s enough to change the test result.
Category: Choosing the Distribution
Question 9
Crossing the two possible truths about H0 with the two possible decisions gives 4 possible outcomes of a hypothesis test.
Missing Word
4
H0 is either true or false, and the decision is either to reject it or not, giving four outcomes. Two are correct decisions, one is a Type I error, and one is a Type II error.
Category: Type I and II Errors
Question 10
With a small sample, the one-sample t test assumes approximate normality of the population being sampled.
Missing Word
normality
Normality means the population values follow a roughly normal, bell-shaped distribution. With small samples the t test depends on it; with large samples the central limit theorem makes the sample mean close to normal anyway.
Category: Choosing the Distribution
Question 11
The normal approximation used when testing a claim about p needs enough expected successes and failures in the sample.
Missing Word
successes
A success is an outcome that has the trait being counted. The normal curve approximates the binomial well only when the sample is expected to contain enough of both outcomes.
Category: Choosing the Distribution
Question 12
The observations in a one-sample test should be independent, meaning that one value gives no information about another.
Missing Word
independent
Independent observations do not influence each other, which a simple random sample helps ensure. The standard error formulas used in these tests depend on this condition.
Category: Choosing the Distribution
Question 13
A one-sample z test of a mean can be used only when the population standard deviation, written with the Greek letter sigma, is known.
Missing Word
sigma
Sigma is the symbol for a population standard deviation. When it is known, the test statistic follows the standard normal distribution; when it must be estimated by the sample standard deviation s, Student's t distribution is used instead.
Category: Choosing the Distribution
Question 14
In H0: p = 0.60, the letter p stands for a population proportion, the share of the population with the trait, written as a decimal between 0 and 1.
Missing Word
proportion
A population proportion, written p, is the fraction of a population with a certain trait, expressed as a number from 0 to 1. A claim such as 'at least 60% of customers are satisfied' becomes a statement about p and is tested with a one-proportion z test.
Category: Setting Up Hypotheses
Question 15
A very small p-value is regarded as strong evidence against the null hypothesis.
Missing Word
evidence
Evidence here means support from the data for rejecting H0. The smaller the p-value, the less likely the observed result would be if H0 were true, and the stronger the case against H0.
Category: P-Values and Decisions