Question

Of some randomly selected Starburst candies in my Amazon-bought package, 27 are orange, 8 are red,
15 are yellow, and 10 are pink.
(a) Let po, pr, py, and pp denote the proportions of orange, red, yellow and pink candies in the
Starburst package respectively. For the test if whether or not there are equal numbers of orange,
red, yellow and pink candies in the package, state the null and alternative hypotheses, in terms
of po, pr, py, and pp.
(b) Calculate the test statistic and p-value for the test above. Is there evidence to suggest that the
number of candies are not equal? If yes, what is the smallest at which the test is signicant?
1

Answer 1

Here chi sqauer test will be used.

(a)

If the proportions of orange, red, yellow and pink candies in the Starburst package are equal then each proprotion should be equal to

po = pr = py = pp =0.25

The hypotheses are:

(b)

Following table shows the calculations:

	O	p	E=p*60	(O-E)^2/E
Orange	27	0.25	15	9.6
Red	8	0.25	15	3.266666667
Yellow	15	0.25	15	0
Pink	10	0.25	15	1.666666667
Total	60		60	14.53333333

The test statistics is:

Degree of freedom: df=4-1=3

The p-value is: 0.0023

Since p-value is less than 0.01 so we reject the null hypothesis.

That is there is evidence to suggest that the number of candies are not equal.