23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis and the alternative hypothesis. 2. Collect and summarize the data into a test statistic. 3. Use the test statistic to determine the p-value. 4. The result is statistically significant if the p-value is less than or equal to the level of significance.

HYPOTHESIS TESTING STEP 2: SET CRITERIA FOR DECISION Alpha Level/Level of Significance probability value used to define the (unlikely) sample outcomes if the null hypothesis is true; e.g., α = .05, α = .01, α = .001 Critical Region extreme sample …

Example 7.2.1 Page 223 Researchers are interested in the mean age of a certain population. A random sample of 10 individuals drawn from the population of interest has a mean of 27. Assuming that the population is approximately normally distributed with variance 20,can we conclude that the mean is different from 30

The test statistic is a one-number summary of all the information in the sample regarding the correctness of the alternative hypothesis. Different kinds of hypothesis tests (e.g., about means, proportions, differences of means, differences of proportions, etc.) require different test statistics. Soon we shall list many standard cases.

Hypothesis Testing • Is also called significance testing • Tests a claim about a parameter using evidence (data in a sample ... Another example: IQ testing • Let X represent Weschler Adult Intelligence scores (WAIS) • Typically, X ~ N(100, 15) • Take i.i.d. samples of …

hypothesis if the computed test statistic is less than -1.96 or more than 1.96 P(Z # a) = α, i.e., F(a) = α for a one-tailed alternative that involves a < sign. Note that a is a negative number. H0: p = .5 HA: p < .5 Reject the null hypothesis if the computed test statistic is less than -1.65 Introduction to Hypothesis Testing - Page 5

Hypothesis Testing Steps Objectives In this chapter, you learn: (Slide 9) The basic principles of hypothesis testing How to use hypothesis testing to test a mean or proportion The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are seriously violated Define Type I and Type II errors.

no reason to doubt that the null hypothesis is true. Similarly, if the observed data is “inconsistent” with the null hypothesis (in our example, this means that the sam-ple mean falls outside the interval (90.2, 109.8)), then either a rare event has occurred (rareness is judged by thresholds 0.05 or 0.01) and the null hypothesis is true,

I Understanding a pdf is all we need to understand hypothesis testing I Pdfs are more intuitive with continuous random variables instead of discrete ones (as from example 1 and 2 above). Let’s move now to continuous variables Michele Pi er (LSE)Hypothesis Testing …

Example 4.2 A coin is tossed and we hypothesise that it is fair. Hence 1 0 is the set 2 containing just one element of the parameter space = [0 ;1]: As a convention we shall denote the complement of 0 in by 1. We call the original hypothesis that 2 0 the null hypothesis and denote it by H 0:The hypothesis that