Question

First impressions 

As part of a survey, a random sample of 1008 Americans was asked, "What do you notice first when you meet someone?" The five possible options to select were as follows:

 1. Smile 2. Eyes 3. Smell 4. Clothes 5. Hair 

The results of the survey are shown in the graphic below. 

What people notice first when they meet someone Hair Smile 47% Eyes 31% Clothes Smell 7% 11% Source: XL for Tips Sonicare survey of American adults

One question of interest is whether or not the survey results match the parameters of the US population, which are given below: Smile -50% Eyes - 30% Smell - 10% Clothes - 5% Hair - 5%

1a. Using complete sentences, clearly explain why this is a chi-square Goodness of Fit Test and not a chi-square Test for Association (Independence).

1b. Clearly state the null and alternative hypotheses for this test. Use the correct statistical notation in your answer

Answer 1

(a) In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval.

(b) The hypothesis being tested is:

H₀: The survey results match the parameters of the US population

H_a: The survey results do not match the parameters of the US population