Question

Companies that produce candies typically offer different colors of their candies to provide consumers a choice. Presumably, the consumer will choose one color over another because of taste. Chance (Winter 2010) presented an experiment designed to test this taste theory. Students were blindfolded and then given a red or yellow Gummi Bear to chew. (Half the students were randomly assigned to receive the red Gummi Bear and half to receive the yellow Bear. The students could not see what color Gummi Bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 121 students who participated in the study, 97 correctly identified the color of the Gummi Bear.

a. If there is no relationship between color and Gummi Bear flavor, what proportion of the population of students would correctly identify the color?

b. Specify the null and alternative hypotheses for testing whether color and flavor are $\mathit{\alpha }\mathbf{=}\mathbf{.}\mathbf{01}$related.

c. Carry out the test and give the appropriate conclusion at Use the p-value of the test, shown on the accompanying SPSS printout, to make your decision.

Short answer

a. The proportion of the population of students who would correctly identify the color is 0.5.

b.The hypotheses are$H_0:p=0.50$and$H_a:p\ne 0.50$

c. At a 1% significance level, we have sufficient evidence to conclude a significant relationship between color and flavor.

Step-by-step solution

Given information

As per the study, out of 121 students who participated, 97 correctly identified the color.

That is

The size of the sample$n=121$

The sample proportion is

$$\begin{gathered} \hat{p}=\frac{97}{121} \\ =0.802 \end{gathered}$$

Calculating the proportion

If there is no relationship between color and Gummi Bear flavor, then each student can make a correct guess or wrong.

Hence the proportion of the population of students would correctly identify the color 0.5.

Setting up the hypotheses

We have to test whether color and flavor are related or not.

That is, we have to test whether the true proportion of students who correctly identified the color of the Gummi Bear is 0.5 or not.

The null and alternative hypotheses are given as

$H_0:p=0.5$

That is, there is no significant relation between color and flavor.

And

$H_a:p\ne 0.50$

That is, there is a significant relation between color and flavor.

Conclusion using p-value

As per the SPSS printout, the p-value is 0.000

That is

$p-value=0.000<0.01$

That is, the p-value is less than the significance level.

Hence, we reject the null hypothesis.

Conclusion:

At a 1% significance level, we have sufficient evidence to conclude that there is a significant relation between color and flavor.