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 11% Source: XL for Philips Sonicare survey of American adults

only answer i need is p-value. thank you!!

Answer 1

For k - 1 = 4 degrees of freedom, the p-value for the given chi square test statistic value here is obtained from the chi square distribution tables as:

$p = P(\chi^2_4 > 10.345 ) = 0.035$

Therefore 0.035 is the required p-value here.

As the p-value here is 0.035 < 0.05, therefore the test is significant here and we can conclude at 5% level of significance here that there is a difference in sample and population proportions distributions here.