Question

Suppose the sales team at Apple is interested in investigating whether the colours of the iPod Touch have any impact on sales. To test this, they use five different colours for the new iPod Touch. The following table shows the number of each colour of 1335 iPods sold during the first month at one retailer. At the 1% significance level, test whether the number of iPods sold in each colour is uniform. Keep 4 decimal places for intermediate calculations.

iPod colour	iPods sold
Grey	290
White	235
Pink	290
Lime	280
Teal	240

Please provide correct answers without using excel formulas. thanks.

Answer 1

As we are testing here whether number of iPods sold in each colour is uniform, therefore the expected number of ipods sold for each colour here is computed as:

= Total ipods sold / 5

= 1335/5

= 267

Using the above expected value, the chi square test statistic here is computed as:

The computations are made in the following table here:

Ipod Colour	Ipods Sold(O_i)	E_i	(O_i - E_i)^2/E_i
Grey	290	267	1.981
White	235	267	3.835
Pink	290	267	1.981
Lime	280	267	0.633
Teal	240	267	2.730
	1335	1335	11.161

Therefore 11.161 is the required chi square test statistic value here.

For n - 1 = 4 degrees of freedom, we get the p-value from the chi square distribution tables here as:

As the p-value here is 0.02 > 0.01 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we don't have sufficient evidence that the distribution of the 5 colours is not uniform here.