Hypothesis Test For Multiple Population Proportions

Question

Consumer Reports took a survey of users of two major mobile phone companies. They asked if the individuals were satisfied with their phone service. Consider the following table

	Samsung	Apple	Motorola
Satisfied	250	300	100
Unsatisfied	85	190	65

a)     What is statistic for the test of multiple population proportions? 

b)     What is the null hypothesis and what distribution is used when testing the null hypothesis? 

c)     Is there sufficient evidence to reject the null hypothesis for this test at the 95% level? 

Answer 1

This would be a chi-square test using the chi-square statistic.

Ho: proportion of satisfied/unsatisfied the same for all 3 phone companies

Ha: at least one proportion different

critical value is chi-square for alpha 0.05 and 2 DOF = 5.99

chi-square stat = sum (O-E)^2/E, summed over each of the 6 cells

Samsung Apple Motorola

Satisfied 250 300 100 650

Unsatisfied 85 190 65 340

335 490 165 990

example of how to compute expected for Samsun/Satisfied cell: 335 * 650/990