A survey was completed by 446 students at a large university in the fall of 2003. Students were asked to pick their favorite color from black, blue, green, orange, pink, purple, red, yellow.

a. If colors were equally popular, what proportion (to three decimal places) of students would choose each color?

b. Pick a color that you suspect will be more popular than others. Using software to access the survey data, report the sample proportion who preferred the color you chose.

c. Tell whether or not your sample proportion is in fact higher than the proportion you calculated in part (a).

d. Use software to produce a 95% confidence interval for the proportion of all students who would choose that color.

e. Does your confidence interval contain the proportion you calculated in part (a), or is it strictly above, or strictly below?

f. Tell whether a 90% confidence interval would be wider or narrower than the interval you produced in part (d).

g. Software should be used to carry out a hypothesis test to see if the sample proportion choosing your color was high enough to assert that, overall, students picked that color more than if they were choosing at random from eight colors. Report the standardized sample proportion z.

h. Report the P-value.

i. State your conclusions, using 0.05 as the cutoff for small P-values.