Use a 0.05 Significance level to test the claim that 20% of all skittles candies are red. 243 skittles were red out of 1245 skittles. 

Expert Answers
embizze eNotes educator| Certified Educator

We are told that 243 of 1245 skittles(tm) are red, and we are asked to test the claim that 20% of skittles are red at the .05 significance level.

(1) The null hypothesis is H0: 20% of skittles are red. (The claim)

The alternative hypothesis H1: The true percentage is not 20%.

(2) This is a two-tailed test. Since we are dealing with proportions we use a z-test to find the critical value(s) and the critical region(s):

For alpha = .05 we have critical values of -1.96 and 1.96. (These are from a standard normal table; the area to the left of z=-1.96 is approximately .025, while the area to the right of z=1.96 is approximately .025.)

(3) To compute the test value we take the observed value  (approximately .1952) minus the expected value (.2); divide this by the standard error which is given by the square root of the product of p (.2), 1-p (.8) divided by n=1245. Thus the test value is -.0048/.0113 or z=-.425

(4) The test value is not in the critical region (-1.96<-.425<1.96 ) so we do not reject the null hypothesis.

(5) There is insufficient evidence to reject the claim that 20% of skittles are red.

** My calculator gives the p-value as .6707; since this is greater than alpha we do not reject the null hypothesis as above.