Question

In: Statistics and Probability

A survey was conducted in five countries. The percentages of respondents whose household members own more...

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.

Solutions

Expert Solution

(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


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