Question

The following tables show figures on the market share of cable modem, DSL, and wireless broadband from a 2002 survey and a 2006 survey which was based on a random sample of 1000 home broadband users. Conduct a goodness-fit-test to test whether the population proportions have changed since 2002, using the critical value method, and level of significance is 0.05. 1. 2002 Survey 2006 Survey Category Cable Modem 67% 410 DSL 2890 500 Wireless/other 90 5%

Answer 1

H0:Null Hypothesis: Population proportions have not changed since 2002

HA: Alternative Hypothesis Hypothesis: Population proportions have changed since 2002

The Test Statistic $\chi ^{2}$ is got as follows:

Category	Observed (O)	Expected (E)	(O - E)2/E
Cable Modem	410	1000X67/100=670	100.8955
DSL	500	1000X28/100=280	172.8571
Wireless/ Other	90	1000X5/100=50	32
Total = $\chi ^{2}$ =			305.7526

ndf = n - 1 = 3 - 1= 2

$\alpha$ = 0.05

From Table, critical value of $\chi ^{2}$ = 5.9915

Since the calculated value of $\chi ^{2}$ = 305.7526 is greater than critical value of $\chi ^{2}$= 5.9915, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that population proportions have changed since 2002.