Topics: Essentials Hypotheses Testing Examples Hypothesis Testing Topics: Essentials Hypotheses Testing Examples

Essentials: Hypothesis Testing (Testing Claims.) What is a hypothesis. Null vs. Alternative hypotheses Statistical Significance: Critical Values & p-values One-sample Tests for mean & proportions

What is a Hypothesis In statistics, a hypothesis is a claim or statement about a characteristic of a population. A Null Hypothesis, denoted Ho, is a statistical hypothesis that contains a statement of equality such as . The Alternative Hypothesis, denoted Ha, is the compliment of the null hypothesis. It is a statement that must be true if Ho is false and it contains a statement of inequality, such as .

Null Hypothesis: A statement that nothing interesting is happening – that there is no difference between observed data and what was expected. The p-value: level at which you are testing a hypothesis; the probability that the data would be at least as extreme as those observed if the null hypothesis were true. Type I Error (a error): the probability of rejecting a null hypothesis when in fact it is true.

Testing the Hypothesis There are two basic approaches to testing a hypothesis. 1) p-value approach 2) critical value approach Similar to when we calculated confidence intervals, the formula used depends upon the characteristics of the sample. These formulas result in a test statistic which is then examined at a given significance level.

Age of patients: The admissions office at Memorial Hospital recently stated that the mean age of its patients was 46 years. A random sample of 120 ages was obtained from admissions office records in an attempt to disprove the claim. Is a sample mean of 44.2 years, with a standard deviation of 20 years, significantly smaller than the claimed 46 years at the a = .10 level of significance?

Hamburger Fat Content: A restaurant claims that its hamburgers have no more than 10 grams of fat. You work for a nutritional health agency and are asked to test this claim. You find that a random sample of nine hamburgers has a mean fat content of 13.5 grams and a standard deviation of 5.8 grams. At a = 0.10, do you have evidence to reject the restaurant’s claim?

Genetically Modified Foods: An environmentalist claims that more than 58% of British consumers want supermarkets to stop selling genetically modified foods. You want to test this claim. You find that in a sample of 100 randomly selected British consumers, 61% say that they want supermarkets to stop selling genetically modified foods. At a = 0.10, can you support the environmentalist’s claim?