Hypothesis Testing of a Single Mean and Single Proportion Quiz

PDF page 560: hypothesis a statement about the value of a population parameter; in the case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation H0) and the contradictory statement is called the alternative hypothesis (notation Ha) hypothesis testing based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected level of significance of the test probability of a Type I error (reject the null hypothesis when it is true) Notation: α. In hypothesis testing, the level of significance is called the preconceived α or the preset α.

PDF page 561: otherwise. The null statement must always contain some form of equality (=, ≤, or ≥).

PDF page 561: equals symbols, i.e., (≠, >, or <).

PDF page 561: In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected. The probabilities of these errors are denoted by the Greek letters α and β, for a Type I and a Type II error respectively. The power of the test, 1 – β, quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.

PDF page 561: 1. α > p-value, reject the null hypothesis.

PDF page 562: If α ≤ p-value, then do not reject H0. If α > p-value, then reject H0. α is preconceived. Its value is set before the hypothesis test starts. The p-value is calculated from the data.

PDF page 561: In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected. The probabilities of these errors are denoted by the Greek letters α and β, for a Type I and a Type II error respectively. The power of the test, 1 – β, quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.

PDF page 561: conclusion using English sentences. Notice that in performing the hypothesis test, you use α and not β. β is needed to help determine the sample size of the data that are used in calculating the p-value. Remember that the quantity 1 – β is called the Power of the Test. A high power is

PDF page 562: If there is no given preconceived α, then use α = 0.05.

PDF page 562: • Single population mean, known population variance

PDF page 562: (or standard deviation): Normal test.

PDF page 562: • Single population proportion: Normal test.

PDF page 562: α = probability of a Type I error = P(Type I error) =

PDF page 562: probability of rejecting the null hypothesis when the null hypothesis is true.

PDF page 562: H0 and Ha are contradictory.

PDF page 560: normal distribution a bell-shaped continuous random variable X, with center at the mean value (μ) and distance from the center to the inflection points of the bell curve given by the standard deviation (σ) We write X ~N(μ, σ) . If the mean value is 0 and the standard deviation is 1, the random variable is called the standard normal distribution, and it is denoted with the letter Z. p-value the probability that an event will happen purely by chance assuming the null hypothesis is true; the smaller the p-value, the stronger the evidence is against the null hypothesis standard deviation a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation