Question

A survey was conducted in five countries. The percentages of respondents whose household members own more than personal computer, laptop, notebook or iPad are as follows:

Australia	53%
New Zealand	48%
China	38%
Japan	54%
South Korea	49%

Suppose that survey was based on 500 respondents in each country.

(a) At the 0.05 level of significance, determine whether there is some significant difference in the proportion of households in these countries who own more than one computer (personal computer, laptop, notebook or iPad).

(b) Find the approximate p-value of the test in (a) from the relevant statistical table.

Answer 1

(a) The null hypothesis

H0: there is no difference in proportion of households in these countries who own more than one computer .

Test statistic ,

(Oi - Ei)2

where Oi : observed frequency

Ei : expected frequency

Oi	Ei	(Oi-Ei)^2/Ei
265	242	2.18595041
240	242	0.01652893
190	242	11.1735537
270	242	3.23966942
245	242	0.03719008
1210	1210	16.6528926

therefore

$\chi ^{2}=16.653$

At 0.05 level of significance with df =4

$\chi ^{2}_{0.05}=9.488$

Since test statistic > critical value , we reject H0.

There is sufficient evidence to conclude that , there is some significant difference in the proportion of households in these countries who own more than one computer.

(b) For $\chi ^{2}=16.653$ with 4 df ,

0.002 < P value < 0.005

We find approximate P value from chi square table

As $\chi ^{2}_{0.005}=14.860$ and $\chi ^{2}_{0.002}=16.924$ with 4 df