In: Statistics and Probability
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.
(a) The null hypothesis
H0: there is no difference in proportion of households in these countries who own more than one computer .
Test statistic ,
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
At 0.05 level of significance with df =4
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 with 4 df ,
0.002 < P value < 0.005
We find approximate P value from chi square table
As and with 4 df