Lecture 5 Tests About Proportions STAT 3120 Statistical Methods I

The testing formula for a one sample proportion is a simple z calculation: Z = (sample estimate – Null value)/Null Standard Error For a proportion, this would be: Z=(p-p o )/SQRT((p o (1-p o )/n) STAT3120 – Tests about Proportions

If 30% of cars on a street are found to be speeding, the city will install “traffic calming” devices. John used his radar gun to measure the speeds of 400 cars on his street. He found that 32% were speeding. Will John get “traffic calming” devices on his street? STAT3120 – Tests about Proportions

Answer the following: 1.Identify the Null and Alternative Hypotheses 2.Identify the Type I and Type II errors, including the implications 3.What is an appropriate alpha value? 4.What is the associated p-value? 5.What is your conclusion? STAT3120 – Tests about Proportions

A recent news article from “VEG World” reported that at least 5% of all American Teenagers eat a vegetarian diet. A sample of 200 teenagers was interviewed about their diets. 8% indicated that they eat vegetarian. Does this prove Veg World’s claim? STAT3120 – Tests about Proportions

Answer the following: 1.Identify the Null and Alternative Hypotheses 2.Identify the Type I and Type II errors, including the implications 3.What is an appropriate alpha value? 4.What is the associated p-value? 5.What is your conclusion? STAT3120 – Tests about Proportions

2. Two Sample Test - compares the proportion of the first sample minus the proportion of the second sample to a given number. It is of common interest to test of two population proportions are equal. e.g. Is there a difference in the percentage of students who pass a standardized test between those who took a prep course and those who did not? Formal Hypothesis Statement examples: H 0 : p a - p b =0 H 0 : p a - p b <0 H 1 : p a - p b  0 H 1 : p a - p b > 0 STAT3120 – Tests about Proportions

Before you undertake a two sample test, there are few things to be determined: 1.The two samples must be independent 2.The number of individuals with each trait of interest and the number without the trait of interest must be at least 10 in each sample. See page 529 for the formula.

STAT3120 – Tests about Proportions Suppose that a random sample of 50 men and 50 women were asked if they make a list before they go to the grocery store. Of these 20 of the men and 30 of the women said “yes”. What do you conclude?

STAT3120 – Tests about Proportions Answer the following: 1.Identify the Null and Alternative Hypotheses 2.Identify the Type I and Type II errors, including the implications 3.What is an appropriate alpha value? 4.Using the formula on page 529, determine the test statistic. What is the associated p-value? 5.What is your conclusion?