Hypothesis Testing of a Single Mean and Single Proportion Quiz

PDF page 542: Hypothesis a statement about the value of a population parameter, in 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. 2 Normal Distribution −(x − μ) 2 2σ

PDF page 543: otherwise. The null statement must always contain some form of equality (=, ≤ or ≥)

PDF page 543: 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 542: Type 1 Error The decision is to reject the null hypothesis when, in fact, the null hypothesis is true.

PDF page 543: Type 2 Error The decision is not to reject the null hypothesis when, in fact, the null hypothesis is false.

PDF page 544: probability of not rejecting the null hypothesis when the null hypothesis is false.

PDF page 544: α = probability of a Type I error = P(Type I error) =

PDF page 543: 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 542: standard normal distribution. 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.

PDF page 542: standard normal distribution. 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.

PDF page 543: 1. α > p-value, reject the null hypothesis

PDF page 544: 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 544: • Single population mean, unknown population

PDF page 544: variance (or standard deviation): Student's t-test.

PDF page 544: • Single population proportion: Normal test.

PDF page 543: 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 544: 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 is used in calculating the p-value. Remember that the quantity 1 – β is called the Power of the Test. A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same.If the power is

PDF page 544: If there is no given preconceived α, then use α = 0.05.