Preference: Color What is your favorite color? A large survey indicates that most people prefer the color Blue. In fact, about 24% of the population claim blue is their favorite color. Suppose a...

Preference: Color  What is your favorite color?  A large survey indicates that most people prefer the color Blue.  In fact, about 24% of the population claim blue is their favorite color.  Suppose a random sample of  n = 56 college students were surveyed and r = 12 of them said that blue is their favorite color.  Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05.

1. What is the level of significance? State the null and alternate hypotheses.


2. What sampling distribution will you use? Do you think the sample size is sufficiently large?    Compute the value of the sample test statistic and corresponding z value.


3. Find the
   P-value of the test statistic. Sketch the sampling distribution and show the area corresponding to the
   P-value.


4. Based on your answers in parts (a), (b), and (c), will you reject or fail to reject the null hypotheses? Are the data statistically significant at level α?


5. Interpret your conclusion in the context of the application.