Question

quest 22

A raincoat manufacturer wants to know if there is a preference for a particular color over other other colors. They randomly survey 64 customers about the color that they would choose yielding the following Color Yellow Red Green Blue # Sold 17 22 13 12 Test the claim that there is no preference to raincoat color. Compute the p-value correct to 3 significant decimal places .547 .205 .275 .0777 .177

Answer 1

Hypotheses are:

We want to test whether all colors have same preference than null hypothesis is:

H0: All colors have same preference.

The alternative hypothesis is:

Ha: At least one color have different preference.

There are 64 cutomers and 4 colors of raincoat. If all colors have same prefrence then expected frequency of each color is

E = 64/4 =16

Following table shows the calculations:

O	E	(O-E)^2/E
17	16	0.0625
22	16	2.25
13	16	0.5625
12	16	1
Total		3.875

Degree of freedom:

df=4-1=3

The p-value is: 0.275

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

That is there is evidence to conclude that there is no preference to raincoat color.